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Mr. Trump’s tweets began just moments after a Fox News report by Mike Tobin, a reporter for the network, about protests in Minnesota and elsewhere. The report featured a protester from Virginia saying “those of us who are healthy and want to get out of our house and do business, we need to get this going again. It’s time.”

The message of support for those efforts from Mr. Trump is radically different from the one he delivered from the White House on Thursday evening. During a briefing for reporters, the president unveiled guidelines that governors could use to decide when it was safe to phase out restrictions to minimize the chance of a resurgence of the dangerous pathogen.

“We are not opening all at once, but one careful step at a time,” Mr. Trump said Thursday after telling governors earlier in the day that “you’re going to call your own shots.”

When he was asked about the protesters during Thursday’s briefing, the president expressed sympathy for the plight of people who are affected by the restrictions, saying that “it’s been a tough process for people. You know, I told you this: There’s death and there’s problems in staying at home too. It’s not just, ‘Isn’t it wonderful to stay at home?’ They’re having — they’re suffering.”

But he ducked the question of whether he would urge the protesters to listen to local authorities, adding that “I think they’re listening. I think they listen to me. They seem to be protesters that like me and respect this opinion. And my opinion is the same as just about all of the governors.”

Trump and Cuomo spar over the federal response to the outbreak.

Gov. Andrew M. Cuomo of New York and Mr. Trump traded barbs on Friday for more federal assistance to help the state fight the virus, the latest escalation between the two. Mr. Trump lashed out on Twitter telling him to “spend more time ‘doing’ and less time ‘complaining.’”

Mr. Cuomo said another 630 people died of the virus in New York on Thursday, according to official state figures, bringing the total confirmed death toll to 12,822.

The daily number of deaths, Mr. Cuomo said, “refuses to come down dramatically,” adding that the toll was “breathtaking in its pain and grief and tragedy.”

“Stop talking!” Mr. Trump wrote as he cited the federal assistance New York has already received — “far more money, help and equipment than any other state.”

Mr. Cuomo hit back mid-briefing and criticized the president for dismissing the need to give help to the states, especially when it comes to the magnitude of tests states need to safely lift restrictions.

Mr. Cuomo said again that the state could not fully reopen its economy without more widespread testing, which would require both supplies and an operational capacity that the health system did not currently have. “We cannot do it without federal help,” he said.

As it is now, he said, “We don’t have a testing system that can do this volume or that can be ramped up to do this volume.”

Mr. Cuomo again declined to predict a timeline for when the state would reopen, pointing out that how the rate at which the infection appeared to be spreading in New York was not yet low enough to say the outbreak was fully under control.

“You’ll see states that have less of a problem opening sooner,” he said. “That is undeniable and totally logical. It depends on that state.”

The governor also said he would issue an executive order directing laboratories in New York to work with the state Health Department to ensure they were prioritizing diagnostic testing. And with growing concern about the number of deaths in nursing homes, he said he will issue an executive order requiring nursing homes to tell families when there are virus cases in their facilities.

Mr. Cuomo, who has extended the state’s broad shutdown until at least May 15, made his daily appearance hours before the start of a mandate for people in New York to wear face coverings in public places where they cannot keep six feet away from others. In buses and subways as well as in for-hire vehicles, everyone, including the driver or operator, must wear a covering, he said. The rule also applies to children as young as 2 years old.

The Centers for Disease Control and Prevention recommends that people wear cloth face coverings to protect those around them, a move that came after research showed that many people were infected but did not show symptoms. (Public health officials have warned against buying or hoarding the N95 masks needed by health care workers.)

Health officials have urged people to combine face coverings with social distancing, suggesting that one tactic did not replace the need for the other.

Governors in Texas, Michigan, Wisconsin, Idaho and other states are looking to ease restrictions, despite inadequate testing.

Texas will let all stores in the state open next week for “retail-to-go,” permitting pick-up and delivery but not in-store shopping. Minnesota will allow golf courses and driving ranges to reopen this weekend. Vermont will let its farmers’ markets reopen on May 1.

Around the country, governors began announcing plans to ease restrictions in their states on Friday, even as cases continue to surge in some parts of the country and inadequate testing will make it difficult for them to identify and contain future outbreaks.

They are taking action as Mr. Trump, who has been impatient to restart the economy, issued a set of guidelines Thursday offering suggestions of when and how to reopen.

The governors are grappling with mounting economic damage and hardship caused by the pandemic. But their moves to tentatively let some businesses reopen is getting underway as the national death toll remains high. Public health experts are warning against acting too soon, fearing new waves of outbreaks that will be difficult to identify early on unless testing is significantly ramped up. But many states and localities are beginning to ease restrictions.

In Texas, Gov. Greg Abbott, a Republican, outlined his plans Friday for “retail-to-go” shopping, and also said that he would lift restrictions on some medical procedures and reopen state parks while requiring masks and social distancing.

But Mr. Abbott announced that the group working to reopen Texas — which he described as a “strike force” — had determined that it would be unsafe for children to return to school, so schools will remain closed for the remainder of the school year. The governor said that he would announce more reopening April 27, and still more in May.

In Minnesota, Mr. Walz, a Democrat, said Friday that golf courses and driving ranges could reopen Saturday morning, and many other outdoor activities could resume, too, including boating, fishing, hunting, and hiking. Some businesses that support those activities, including bait shops, shooting ranges and game farms, can also open. But campgrounds, recreational equipment rental, charter boats, and guided fishing will remain closed.

In Michigan, Ms. Whitmer, who imposed one of the strictest stay-at-home orders in the nation, said Friday that she hoped to loosen the regulations in two weeks’ time, on May 1.

Ms. Whitmer, a Democrat who has faced criticism from some residents and business leaders, said that any decision would depend on what the data on infections says as that date approaches. Her state trails only New York and New Jersey in the number of residents whose deaths have been tied to the virus.

“It’s two weeks away, and the information and the data and our ability to test is changing so rapidly, it’s hard to predict precisely where we’ll be in a week from now, let alone two weeks,” the governor said on ABC’s “Good Morning America” days after thousands of demonstrators, who mostly remained in vehicles, protested outside the State Capitol in Lansing and accused Ms. Whitmer of going too far.

Gov. Phil Scott of Vermont, a Republican, said Friday that he would allow some businesses in the state to reopen by Monday, provided that they involve very low contact and involve no more than two people.

The governor gave the green light to a handful of businesses — property managers, real estate agents and some construction crews — but said they must comply with safety guidelines, such as social distancing and wearing a mask. The state will open its farmer’s markets on May 1st. So far, the state has registered 779 cases and 35 deaths.

Gov. Tony Evers of Wisconsin, a Democrat, said on Thursday that golf courses could open with certain restrictions and that for-hire lawn care could be carried out if it was performed by one person. Stores selling materials to make face masks can open for curbside pickup, he said.

In Idaho, Gov. Brad Little, a Republican, has said businesses that were once deemed nonessential, such as craft stores, candle shops or dog groomers, could open to allow for curbside or delivery services until at least the end of the month. He noted that they should prepare to reopen altogether in May with social distancing and sanitation rules in place.

Gov. Ron DeSantis of Florida, who speaks frequently with Mr. Trump and has faced criticism for his initial piecemeal approach to tackling the virus, said on Friday that he would refer to the White House guidelines on reopening but not necessarily abide by everything they propose.

“We will obviously use that as a kind of baseline,” Mr. DeSantis, a Republican, said at a news conference in Fort Lauderdale. “It doesn’t mean Florida is going to do every single thing they say or not say.”

As of Friday morning, Florida had more than 24,000 cases and nearly 700 deaths.

Some local leaders in Florida are beginning to tiptoe toward reopening. Mayor Lenny Curry of Jacksonville announced on Thursday that beaches and parks in Duval County will reopen at 5 p.m. on Friday, for limited hours, and restricted to social distant recreational activities.

But just as much of the country entered life under quarantine in a patchwork fashion, it is poised to ease restrictions the same varied way, responding to the local needs to fight the virus.

Gov. Gavin Newsom of California, a Democrat, has suggested that restaurant patrons would have to submit to having their temperatures taken before being seated once that state begins a gradual reopening.

More than 22 million Americans have lost their jobs in recent weeks — a toll that roughly matches the entire cumulative workforce of 23 states — and many governors, as well as Mr. Trump, fear the mounting economic repercussions of sustained shutdowns.

But tackling the economic catastrophe requires getting a handle on the public health crisis.

Dr. Deborah L. Birx, the White House’s virus response coordinator, told CNN on Thursday night that surveillance to give communities early warning signs of local transmission would need to be enhanced, diagnostic testing capabilities expanded and contact-tracing efforts bolstered.

“Any one piece by itself will not be able to accomplish what we need,” she said.

The lack of testing presents a serious challenge to reopening, health experts say.

To give people a sense of security as states begin to ease restrictions requires an expanded testing capacity, health experts say, and the country is far behind in conducting enough tests to responsibly inform these decisions.

The ultimate goal is to separate the sick from the healthy so that Americans feel safe returning to a somewhat normal life and the virus does not sweep through communities again, which requires more widespread testing.

The capacity for such testing has been growing, but not fast enough, public health experts say. Supplies continue to run out and some areas are only testing people who present specific symptoms. Tests to determine whether someone has already had the virus are slowly rolling out and most have not been vetted by the Food and Drug Administration.

Without widespread testing and surveillance, said Angela Rasmussen, a virologist at Columbia University in New York, “we won’t be able to quickly identify and isolate cases in which the patients are presymptomatic or asymptomatic, and thus community transmission could be re-established.”

Mr. Trump, whose administration has been criticized for its slow rollout of tests as the virus took hold in the United States, has sought to portray testing as a state responsibility, even as many governors are pleading for more federal help. “The States have to step up their TESTING!” Mr. Trump wrote in a Twitter post on Friday, as New York Gov. Andrew M. Cuomo asked for more help from the federal government to produce tests on a larger scale.

Reopening before those issues are resolved, though, risks endangering the few places that have managed to avoid the worst effects of the virus, and would be accompanied by other significant scientific concerns:

Waiting periods of 14 days are required. States wishing to loosen rules are asked to meet certain criteria every two weeks, but that leaves open the possibility that someone infected toward the end of the 14th day could end up seeding an outbreak as restrictions were lifted.

Shortages of protective equipment persist. Among the greatest fears in reopening parts of the economy is that communities with less restrictions will be at a greater risk for outbreaks, which will create new demands for medical supplies already spread thin.

With social distancing difficult on ships, the crew of the Mercy, a Navy hospital, moves ashore.

Aboard the hospital ship U.S.N.S. Mercy, docked in the Port of Los Angeles, most of the military crew is moving off the ship and into hotels ashore. Sailors will be bussed from their hotels to to work their shifts aboard the Mercy. Navy spokesman Lt. Andrew Bertucci said on Friday that the decision was made in order to better facilitate social distancing.

“The plan is to drastically decrease the amount of contact that the crew has with each other,” Lieutenant Bertucci said. “It will ultimately be safer for both the crew and the patients.”

Between 800 to 900 crew members had been living on the Mercy full-time, but that number will go down to about 100 to 200 in the coming days. On Thursday 150 sailors moved off the ship, and that same number is expected to move to hotels daily through Sunday. Lieutenant Bertucci noted that the crew aboard the U.S.N.S. Comfort, which is docked in New York City, recently moved most of its crew to hotels ashore as well.

The move comes after a total of seven crew members tested positive for Covid-19 since the ship arrived to help area hospitals treat non-Covid patients, and more than 100 of the crew who had been in contact with those seven have moved off the ship into precautionary quarantine. All of the Mercy sailors in quarantine have tested negative for the coronavirus and are regularly monitored in case they were to develop any symptoms.

The commanding officer of the Mercy’s medical treatment team, Capt. John Rotruck, is quarantined aboard the ship in his stateroom after an investigation found that he had been in proximity to a Covid-positive crew member. Captain Rotruck has tested negative for novel coronavirus, and said his ability to continue the ship’s mission is unchanged.

The ship will continue to treat the patients it already has onboard, and will take new patients as requested by local authorities.

Stocks jump as investors rally behind the idea of reopening the economy.

Stocks in the United States rallied on Friday, with efforts to reopen the economy taking center stage and investors undeterred by more data showing the economic damage of the pandemic.

The gains came after President Trump told governors on Thursday that they could begin reopening businesses in their states by May 1 or earlier, and Boeing — one of the nation’s largest manufacturers — said it plans to bring about 27,000 employees back to work in Washington State to resume aircraft production.

The S & P 500 rose about 2 percent in early trading. European markets were also trading 3 to 4 percent higher after an upbeat day in Asia.

After global stock markets nose-dived earlier this year, they have been rebounding since late March, as investors have routinely looked past evidence of the damage caused by stay-at-home orders and business shutdowns, and instead focused on hopes for an eventual recovery.

On Friday, the rally came after China reported that its economy — the world’s second largest — shrank for the first time in decades. And data on car sales in Europe showed they collapsed.

Some also saw hopeful signs in a report by the medical news website STAT that a drug from Gilead Sciences showed early — and, thus far, unproven — promise in fighting the virus. According to STAT, the antiviral drug, remdesivir, has helped patients with severe symptoms recover rapidly in a clinical trial at a Chicago hospital. Gilead’s shares jumped more than 11 percent, making it the best performing stock in the S&P 500.

Still, without data from rigorous trials with control groups, it is impossible to know how effective the drug actually is. The National Institutes of Health is conducting a trial in which patients receive remdesivir or a placebo. The results will be known within weeks.

Epidemiologists still don’t know the worldwide death rate for Covid-19.

Coroners in some parts of the United States are overwhelmed. Funeral homes in virus hot spots can barely keep up. Newspaper obituary pages in hard-hit areas go on and on. Covid-19 is on track to kill far more people in the United States this year than the seasonal flu.

But determining just how deadly the new virus will be is a key question facing epidemiologists, who expect resurgent waves of infection that could last into 2022.

As the virus spread across the world in late February and March, the projection circulated by infectious disease experts of how many infected people would die seemed plenty dire: around 1 percent, or 10 times the rate of a typical flu.

But according to various unofficial Covid-19 trackers that calculate the death rate by dividing total deaths by the number of known cases, about 6.4 percent of people infected with the virus have now died worldwide.

In Italy, the death rate stands at about 13 percent, and in the United States, around 4.3 percent, according to the latest figures on known cases and deaths. Even in South Korea, where widespread testing helped contain the outbreak, 2 percent of people who tested positive for the virus have died, recent data shows.

Those supposed death rates also appear to vary widely by geography: Germany’s fatality rate appears to be roughly one-tenth of Italy’s, and Los Angeles’s about half of New York’s. Among U.S. states, Michigan, at around 7 percent, is at the high end, while Wyoming, which reported its first two deaths this week, has one of the lowest death rates, at about 0.7 percent.

Virology experts say there is no evidence that any strain of the virus, officially known as SARS-CoV-2, has mutated to become more severe in some parts of the world than others, raising the question of why there appears to be so much variance from country to country.

San Francisco’s Chinatown got ahead of the virus.

On Jan. 24, the eve of the Chinese New Year, Dr. Jian Zhang, the chief executive of San Francisco’s Chinese Hospital, saw an alarming photograph on WeChat. An old medical school colleague was about to join more than 100 other health care providers being rushed to Wuhan to help manage the outbreak.

Dr. Zhang immediately recognized the threat.

“Twelve hours,” she recalled thinking. “We have direct flights from Wuhan to San Francisco, and it only takes 12 hours.” She knew those who were visiting family in China during the Lunar New Year would soon be back.

A perfect storm seemed to be headed for the 22 square blocks that make up Chinatown, one of the most densely populated neighborhoods in the United States. Many of the neighborhood’s older residents live in cramped single-room-occupancy hotels. Travel between Chinatown and China is constant.

Given the unpredictable pathways of this highly contagious disease, Dr. Zhang and other leaders in Chinatown are well aware that circumstances could change in an instant. But the neighborhood has thus far held off the virus.

Chinese Hospital, an acute care facility in the heart of the neighborhood, admitted its first Covid-19 patient on March 26, three weeks after patients had been hospitalized in other parts of San Francisco. As of mid-April, at least 34 cases of Covid-19 had been detected in 22 S.R.O.s around San Francisco. None of these cases were within the neighborhood, although three were on its border.

Chinese Hospital was at the center of an effort to coordinate barriers for entry of the virus. These involved almost every major institution in Chinatown, including the Chinese-language press and deeply engaged neighborhood institutions, all of whom were imprinted with memories of earlier infectious disease outbreaks. Deep links to front-line health workers in China were invaluable as Chinese Hospital worked to avoid what everyone thought was coming.

“It’s kind of amazing,” said Aaron Peskin, a San Francisco supervisor who represents the neighborhood. “Chinatown, knock on wood, is looking pretty darn good.”

Those we’ve lost: Israel Sauz, gas-station worker and new father, dies at 22.

Just 21 days later, on April 5, Mr. Sauz was dead. He was 22.

The cause was complications related to Covid-19, the disease caused by the virus, according to family friends and the school district where he attended high school.

Many in Tulsa may not have recognized his name, but they knew the smiling face — he was an assistant night manager at a busy QuikTrip gas station and convenience store about a mile east of downtown Tulsa. He was still a teenager when he first started working for QuikTrip, a popular chain based in Tulsa.

He lived in the Tulsa suburb of Broken Arrow. He and his wife, Krystal, had celebrated their first wedding anniversary two weeks before Josiah was born.

Federal relief funds for small businesses run out, leaving many struggling.

The $349 billion government program meant to keep small businesses afloat during the pandemic and economic meltdown ran out of money on Thursday, even as many small-business owners were desperately trying to apply for loans. Now they are trying to figure out how to keep their businesses alive while Congress negotiates the possible release of additional rescue funds.

Doug Martin, a sports marketer in Long Beach, Calif., approached three banks to try to get a loan through the program. Each turned him down for different reasons. As a last resort, he tried a fourth bank with the help of his financial adviser, but didn’t hear back.

“This morning, I read that the money’s gone, and I’m like, heck, I didn’t even get a shot at this,” Mr. Martin said.

The program, administered by the Small Business Administration through participating banks, was marred by technical glitches from the start, and overwhelming demand and confusion about how it would all work slowed down the approval process. Around the country, would-be borrowers were turned away by banks because there were too many applicants. Some lost valuable time because their bankers didn’t know all the details about how the program would work, while others couldn’t find a lender that would deal with them.

More money is expected to come, but when is an open question. Congressional leaders and the Trump administration were discussing adding hundreds of billions of dollars to replenish the program, but have so far failed to reach an agreement.

Here’s a guide for those in need of financial help.

If your income has fallen or been cut off completely, we’re here to help. Here is some basic information you’ll need to get through the current crisis, including guides to government benefits, free services and financial strategies.

Homemade or more professional: Which mask is best for you?

Face masks have become an emblem in the fight against the virus, with officials in the United States and elsewhere recommending — and in some cases mandating — that people wear them to help slow the spread of the deadly outbreak.

Figuring out what to wear is not so easy. N95 and medical masks, which offer the most protection and are heavily in demand, should be reserved for health care workers who are regularly exposed to infected patients.

Here’s a look at some of the types of masks you might encounter, how they work, what to consider when making your own and the level of protection they could provide.

Spring is prom season. Or at least it was.

For students in the class of 2020, the crisis arrived just as they were receiving college acceptance letters, dreaming about new jobs, gearing up to leave high school — and making plans for prom, which, for most students, has been canceled.

We photographed 10 students from Omaha in the outfits they had planned to wear to the dance. They talked to us about their prom dreams, hopes and disappointments.

The cultural rite of passage, which they’ve largely experienced through movies and television shows, books and Mom’s old photographs, was their chance to feel like adults — or at least like they were on the brink of adulthood — for the first time.

Now, it feels like high school is ending on a whimper.

As virus spreads in U.S. jails, a hard-hit California prison is to get a field hospital.

The Bureau of Prisons is putting a field hospital inside a penitentiary in California that has more inmates with confirmed cases than any other federal prison.

Sixty-nine inmates and 22 staff members at the penitentiary, Lompoc, which is near Santa Barbara, have the virus, according to the bureau. The prison houses about 1,500 male inmates in a medium-security penitentiary and adjacent minimum-security satellite camp.

A spokeswoman for the bureau said the prison was reaching a contract for additional medical staff and a 25-bed mobile hospital that could be expanded up to 100 beds. She added that prison employees were retrofitting unused office space to create isolation rooms for inmates with the most serious cases.

The virus is spreading rapidly in prisons and jails across the country, and critics say efforts to release people are happening too slowly. Hundreds of inmates have been infected at a jail in Chicago and 18 federal inmates have died.

Here’s what else is happening around the world.