The C.D.C. says three feet of distance at elementary schools is enough. The F.B.I. is investigating whether Cuomo aides gave the Justice Department false information about Covid deaths in nursing homes.

The nation has hit a precarious point in the pandemic, as coronavirus cases — significantly down since peaks in January — have plateaued this month to about 55,000 new cases a day, a level public health officials say is still too high.

Even with the accelerated pace of vaccinations, worrisome variants are spreading. Some states, especially on the East Coast, have struggled for weeks to make any progress in reducing cases. At the same time, governors are starting to relax restrictions on businesses like bars, indoor gyms, and casinos, and many Americans are dining in newly reopened restaurants, replanning summer weddings that were abruptly canceled in 2020, and booking spring break trips.

Last week, air travel in the United States rose to its highest level since the pandemic hit, and airline executives said that bookings in the coming months indicate an eagerness from Americans to begin traveling in large numbers again.

The path ahead — and public guidance about how people should behave at this moment — seems uncertain, even contradictory. Epidemiologists said they viewed the current moment in the pandemic as a sprint between vaccinations and newly confirmed cases, particularly those caused by variants that can be more contagious. Dr. Anthony S. Fauci, the nation’s top infectious-disease expert, warned Friday “that it’s really quite risky to declare victory before you have the level of infection in the community to a much, much lower level than 53,000 cases per day”.

“So it is unfortunate, but not surprising, to me that you are seeing increases in several cases per day in areas — cities, states, or regions — even though vaccines are being distributed at a pretty good clip of 2 to 3 million per day,” Dr. Fauci said.

No state is reporting case numbers anywhere near-record levels, and the sort of explosive case growth seen in hard-hit areas through 2020 has almost completely abated. Kansas is averaging about 215 new coronavirus cases a day, down from more than 2,000 in early January. And North Dakota, which has the country’s most known cases per capita, is now regularly adding fewer than 100 cases a day, in a state with a population of 762,000.

But there are warning signs in the data.

Vermont, which escaped the worst of the pandemic in 2020, has struggled all of this year to curb an outbreak. Michigan, which had appeared to bring the virus under control in January, has seen case numbers increase by more than 80 percent over the last two weeks, though they remain well below their December peak. In South Florida, infection levels have remained persistently high, with about 1,000 cases reported each day in a single county, Miami-Dade.

Yet even in states where the virus appeared far from under control, officials have proceeded to lift restrictions on businesses, and companies have pushed for reopenings. New York has more recent cases per capita than everywhere except New Jersey, and the New York City metro area has the country’s second-highest rate of new infections, behind only Idaho Falls, Idaho. On Wednesday, Gov. Andrew M. Cuomo announced that indoor fitness classes may resume on March 22.

In California, around 2,900 cases are reported most days, down from about 40,000 in mid-January. In Southern California, where cases peaked early this winter, officials at Disneyland said that after more than a year of being closed, the theme park would open on April 30 with rules in place limiting capacity.

“I think it is a race against time,” said Dr. Stephen J. Thomas, SUNY Upstate Medical University’s chief of infectious disease. “Every single person that we can get vaccinated or every single person that we can get a mask on is one less opportunity that a variant has”.