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 Protection has warned that 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 stands, many U.S. states are already under tremendous strain. The seven-day rolling average of daily deaths is rising in 30 states and the District of Columbia, and on Monday the U.S. death toll surpassed 398,000, according to data collected by Johns Hopkins University — by far the highest recorded death toll of any country in the world.

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 and universities in the fall.

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 it 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 on Jan. 17.

Rural Yuma County — known as the winter lettuce capital of the U.S. — is now one of the state’s hot spots. Exhausted nurses there are now regularly sending COVID-19 patients on a long helicopter ride to hospitals in Phoenix when they don’t have enough staff. The county has lagged on coronavirus testing in heavily Hispanic neighborhoods and just ran out of vaccines.

But some support is coming from military nurses and a new wave of free tests for farmworkers and the elderly in Yuma County.

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

In some cases, vaccine supplies thus far do not meet demand. More than 172,000 people in Missouri’s St. Louis County have registered for the vaccine, but the the local health department so far has only received 975 doses, said County Executive Sam Page.

In California, the most populous state, counties are pleading for more vaccine as the state tries to reduce a high rate of infection that has led to record numbers of hospitalizations and deaths.

Although the state last week said anyone age 65 and older can start receiving the vaccine, Los Angeles County and some others have said they don’t have enough to immunize so many people. They are concentrating on protecting health care workers and the most vulnerable elderly in care homes first.

On Monday, the superintendent of the Los Angeles Unified School District sent a letter asking for state and county authorization to provide vaccinations at schools for staff, local community members — and for students once a vaccine for children has been approved.

The death rate from COVID-19 in Los Angeles County — an epicenter of the U.S. pandemic — works out to about one person every six minutes. On Sunday, the South Coast Air Quality Management District suspended some pollution-control limits on the number of cremations for at least 10 days in order to deal with a backlog of bodies at hospitals and funeral homes.

In other areas of the country, officials are working to ensure that people take the vaccine once they’re offered it amid concerns that many people are hesitant. Maryland Gov. Larry Hogan, in a livestreamed event on Martin Luther King Jr. Day, received a shot, and urged other Marylanders to do likewise.

“We’re all looking forward to the day we can take off and throw away our masks,” Hogan said. “The only way we are going to return to a sense of normalcy is by these COVID-19 vaccines.”

But challenges to the vaccine campaign are surfacing worldwide.

The World Health Organization chief on Monday lambasted drugmakers’ profits and vaccine inequalities, saying it’s “not right” that younger, healthier adults in some wealthy countries get vaccinated against COVID-19 before older people or health care workers in poorer countries.

Director-General Tedros Adhanom Ghebreyesus lamented that one country received a mere 25 doses while over 39 million doses have been administered in nearly 50 richer nations.

“Just 25 doses have been given in one lowest income country — not 25 million, not 25,000 — just 25. I need to be blunt: The world is on the brink of a catastrophic moral failure,” Tedros said. He did not specify the country, but a WHO spokeswoman identified it as Guinea.