WASHINGTON — The federal government next month will start mailing at-home Covid test kits for free to any U.S. household that requests one, a senior administration official said, as the omicron variant of the coronavirus contributes to a spike in new cases.

The White House is preparing to ship as many as 500 million kits, and it is setting up a website for people to submit their requests, the official said, without specifying how many tests each household can receive or how quickly.

The federal government also plans to set up new testing sites nationwide in addition to the 20,000 already operational, with the first one opening in New York City before Christmas, the official said.

President Joe Biden is scheduled to deliver a speech Tuesday about the administration’s plan to combat the pandemic this winter.

Testing remains one of the biggest challenges for the administration, with long lines forming at testing centers in recent days and at-home rapid tests selling out quickly, public health officials have said.

The U.S. also lags behind other countries in making tests affordable. In some countries, rapid tests sell for as little at $1, whereas a pack of two tests can cost U.S. consumers more than $20. Biden previously directed insurance companies to cover the cost of at-home tests for policyholders, but that still requires upfront costs for consumers, who must file claims and wait to be reimbursed.

In addition to detailing the free testing kits and sites, Biden will announce Tuesday that he is directing 1,000 members of the military to help hospitals shore up their staffing and deploying the Federal Emergency Management Agency to set up overflow operations for hospitals that are at capacity, the official said.

To assist hospitals, the Defense Department will start deploying personnel, including doctors, nurses and medics, to hospitals in need starting next month, the official said. Eight states set hospitalization records Sunday, including Ohio and Wisconsin, according to an NBC News analysis of data from the Department of Health and Human Services.

Biden is expected to discuss the threat posed by the omicron variant, warning that a growing number of vaccinated people are likely to get infected in the coming months. In doing so, he will emphasize that data so far indicate that the Covid vaccines protect against severe disease, particularly when they are combined with booster shots.

“Because omicron spreads easily, we will see fully vaccinated people get Covid-19. But vaccinated people who get Covid will likely have no symptoms or mild symptoms,” the senior administration official said. “Because of that strong protection, the president will tell the American people if they are vaccinated and follow the process that we all know well, especially masking while traveling, they should feel comfortable celebrating Christmas and holidays.”

But Biden is expected to offer a more grim outlook for the 40 million unvaccinated people in the U.S.

“If you are unvaccinated, you are at high risk of getting sick,” the official said. “This variant is highly transmissible, and the unvaccinated are eight times more likely to be hospitalized and 14 times more likely to die from Covid.”

There are still many unknowns about the omicron variant, which now accounts for the majority of new cases in the U.S. Top health officials have said it is more contagious than the delta variant, which was already significantly more transmissible than the alpha variant. It is unclear whether the omicron variant is more lethal, but even if a smaller percentage of those infected become severely ill, its highly contagious nature could result in just as many or more deaths compared to previous variants.

Some hospitals are also struggling to use all available tools to fight the pandemic. Facilities in New York said they are no longer able to offer monoclonal antibody treatments because they have run out of supplies, particularly a treatment from GlaxoSmithKline that has been shown to work against the omicron variant.

The Department of Health and Human Services said that it paused distribution of the antibodies but that hospitals will begin receiving GlaxoSmithKline’s sotrovimab antibody treatment as early as Tuesday. The current supply of sotrovimab is limited, but the U.S. expects to have 300,000 additional doses next month, an agency spokesperson said.

CORRECTION (Dec. 21, 8:25 a.m.): A previous version of this article misstated the number of new testing sites the Biden administration plans to set up during the latest surge. The exact new number is unknown, not 20,000, the number of sites currently operational.