As states loosen restrictions and variants spread, Fauci warns that the U.S. could be headed for yet another virus spike.

States have continued steadily lifting restrictions, despite warnings from top federal health officials like Dr. Anthony S. Fauci that new coronavirus cases in the United States have plateaued at a very high level after their drastic drop has stalled, and that the country urgently needed to contain the spread of more transmissible variants.

Arizona, California and South Carolina joined a growing list Friday by loosening restrictions, to varying degrees. Arizona’s governor ended capacity limits on businesses, but said they must still require masks. South Carolina’s Republican governor lifted the state’s mask mandate in government buildings, while recommending restaurants continue requiring masking.

California will allow amusement parks and outdoor sports and live events at stadiums to restart on April 1, with reduced capacity and mandatory masks.

“We’ve just now recently experienced the worst surge,” Dr. Fauci said Friday during a White House coronavirus briefing, adding that the country had plateaued at between 60,000 and 70,000 new cases per day. “When you have that much of viral activity in a plateau, it almost invariably means that you are at risk for another spike.”

The seven-day average of new cases was about 61,000 day as of Friday, the lowest average since October, according to a New York Times database. But that number was still close to last summer’s highest peak.

Fatalities are falling, too, in part because of vaccinations at nursing homes. Yet the nation is still routinely reporting 2,000 deaths in a single day.

Dr. Fauci warned the United States could be following the same treacherous path that Europe has recently been on.

“They plateaued,” he said. “And now, over the past week, they saw an increase in cases by 9 percent, something we desperately want to avoid.”

He warned that the virus mutates as it replicates, a process that can be extended when immunocompromised people are infected. He said that maintaining masking, hand washing and social distancing was urgent.

The B.1.1.7 variant, first identified in Britain, is spreading so rapidly in the United States that data analysis suggest that, as of this week, it has most likely grown to account for 20 percent of new U.S. cases. And scientists in Oregon have identified a single case of a homegrown variant with the same spine as B.1.1.7 that carries a mutation that could blunt the effectiveness of vaccines.

Earlier this week, Texas and Mississippi, both Republican-led states, lifted mask mandates. President Biden denounced those moves as “a big mistake” that reflected “Neanderthal thinking,” saying it was critical for public officials to follow the guidance of doctors and public health leaders as the coronavirus vaccination campaign gains momentum.

Other Republicans have been more cautious. Gov. Mike DeWine of Ohio said he would lift all public health measures aimed at curbing the virus crisis, but only once new cases there drop under a certain threshold. In Alabama, Gov. Kay Ivey said she would extend the state’s mask mandate through April 9.

In Arizona, Gov. Doug Ducey has taken what he calls a “measured approach” barring local leaders from enacting measures that shut down businesses and allowing major league sports to restart if they receive approval from the state’s Department of Health Services.

Among Democrats, Gov. Gretchen Whitmer of Michigan said on Tuesday that she was easing restrictions on businesses and would allow family members who had tested negative for the coronavirus to visit nursing home residents. In California, the state’s public health department also loosened some restrictions Friday, saying that amusement parkscould reopen on a limited basis as soon as April 1.

In New York City, limited indoor dining has returned. And on Thursday, Connecticut’s governor said the state would end capacity limits later this month on restaurants, gyms and offices. Masks remain required in both places.

Dr. Rochelle P. Walensky, the director of the Centers for Disease and Prevention, has implored states not to relax their restrictions yet. A new report from the C.D.C. found that counties that allowed restaurants to open for in-person dining in the United States had a rise in daily infections weeks after. The study also said that counties that issued mask mandates reported a decrease in virus cases and deaths within weeks.