NEW YORK - Coronavirus deaths are rising in nearly two-thirds of American states as a winter surge pushes the overall toll toward 400,000 amid warnings that a new, highly contagious variant is taking hold.

As Americans observed a national holiday Monday, New York Gov. Andrew Cuomo pleaded with federal authorities to curtail travel from countries where new variants are spreading.

Referring to new versions detected in Britain, South Africa and Brazil, Cuomo said: “Stop those people from coming here. … Why are you allowing people to fly into this country and then it’s too late?”

The U.S. government has already curbed travel from some of the places where the new variants are spreading - such as Britain and Brazil - and recently it announced that it would require proof of a negative COVID-19 test for anyone flying into the country.

But the new variant seen in Britain is already spreading in the U.S., and the Centers for Disease Control and Prevention has warned it will probably become the dominant version in the country by March. The CDC said the variant is about 50% more contagious than the virus that is causing the bulk of cases in the U.S.

While the variant does not cause more severe illness, it can cause more hospitalizations and deaths simply because it spreads more easily. In Britain, it has aggravated a severe outbreak that has swamped hospitals, and it has been blamed for sharp leaps in cases in some other European countries.

As things stand, many U.S. states are already under tremendous strain. The seven-day rolling average of daily deaths is rising in 30 states, and on Monday the U.S. death toll surpassed 398,000, according to Johns Hopkins University - by far the highest recorded death toll of any country.

Ellie Murray, an assistant professor of epidemiology at the Boston University School of Public Health, said cases have proliferated in part because of gatherings for Christmas and New Year - and compounded previous surges from Thanksgiving and the return of students to schools.

The pace of any further spread will depend on whether those who did gather with family and friends quarantined afterward or went back to school or work in person, she said.

One of the states hardest hit during the recent surge is Arizona, where the rolling average has risen over the past two weeks from about 90 deaths per day to about 160 per day.

“It’s kind of hard to imagine it getting a lot faster than it is right now, because it is transmitting really fast right now,” said Dr. Joshua LaBaer, director of the Biodesign Institute research center at Arizona State University.

Amid the rise in cases, a vast effort is underway to get Americans vaccinated - what Cuomo called “a footrace” between the vaccination rate and the infection rate. But the campaign is off to an uneven start.

According to the latest data, about 31.2 million doses of vaccine have been distributed, but only about 10.6 million people have received at least one dose.