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

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” requiring schools to offer in-person learning no later than March 15, 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 parks could 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.