WASHINGTON — The United States government doubled its order for Pfizer’s Covid pills on Tuesday, a move that will modestly increase the nation’s very limited supply of the treatment in the short term amid a record-setting surge in coronavirus cases.

The new order will eventually provide enough pills for an additional 10 million Americans, bringing the government’s total order of the drug to 20 million treatment courses. But they will not all be available right away. Only 35,000 of the additional courses will be delivered this month, and 50,000 more in February, supplementing 350,000 treatment courses that were already expected over the next two months, according to a senior administration official.

The order underscored how urgently health providers need alternatives to vaccines, as roughly 35 million adults remain without a shot and more vulnerable to severe outcomes from Covid-19. Tens of millions more have been vaccinated but have risk factors that also make them especially vulnerable.

The new order also suggests that the federal pandemic response will increasingly rely on oral treatments, which are scarce and facing intense demand.

“We may need even more,” President Biden said on Tuesday, announcing the move ahead of a Covid-19 briefing he was set to receive from health advisers. “That’s the estimate we need right now.”

The government has agreed to pay Pfizer $530 for each treatment course, the same amount it paid for its initial order late last year, the senior official said.

Monthly deliveries of the Pfizer treatment, known as Paxlovid, are not expected to ramp up into the millions until April, too late to help with the current surge. The company says it takes six to eight months to produce the drug; the combined order is not due to be completely filled until the end of September.

Still, Mr. Biden described the doubled order as a key component of the federal government’s Covid strategy. “They’re a game-changer,” he said, “and have the potential to dramatically alter” the course of the pandemic.

Paxlovid was authorized two weeks ago for use in high-risk Covid patients age 12 or older. Pfizer expects to produce 120 million courses of it in 2022 for all global buyers. The treatment has proved in clinical trials to be highly effective in staving off severe illness when taken soon after the start of symptoms.

Pfizer’s treatment is meant to be taken as 30 pills over five days, with patients taking three pills at a time: two of Pfizer’s pills and one of a low-dose H.I.V. drug known as ritonavir, which helps Pfizer’s drug remain active in the body longer.

But public health experts have warned that without an adequate testing supply — a problem in many parts of the country — it could be difficult to quickly get the pills to those most in need.

Mr. Biden on Tuesday said that in addition to more federal test sites opening, the administration’s plan to have insurers reimburse people for at-home tests would go into effect soon, as would a website allowing Americans to order free tests delivered to their homes, from a pool of 500 million being ordered by the federal government.

“I know this remains frustrating,” he said. “Believe me, it’s frustrating to me. But we’re making improvements.”

The first supplies of Paxlovid have already begun arriving in some parts of the country. The allocations are based on each state’s population, but federal officials are considering shifting that model at some point to one based on case rates and hospitalizations, similar to the system it uses for distributing monoclonal antibody treatments.

Senator Chuck Schumer of New York, the majority leader, urged the federal government over the weekend to adopt such a model. With case counts so high in New York relative to other states, he said, “we deserve to get as many of these antivirals as quickly as possible.”

The Department of Health and Human Services maintains a list of locations where the Pfizer pill is available. For now, supply is so limited that state health officials are recommending it be used only for the patients at highest risk.

The National Institutes of Health, which formulates treatment guidelines for physicians, recommended last month that when supply is limited, antiviral pills and antibody treatments should be prioritized for the highest-risk unvaccinated patients, as well as people of any vaccination status with weakened immune systems.

Many state officials have already taken cues from that guidance, saying they are carefully distributing the pills they have received to people most in need. Arizona, for instance, advised that Paxlovid be given only to people over 70 who also have severe health conditions like end-stage heart disease, or to younger patients with weakened immune systems.

In West Virginia, health officials have shipped around 20 treatment courses to each of 14 locations and reserved about 20 more in case of an outbreak, said Dr. Clay Marsh, the state’s Covid-19 czar.

And in Louisiana, health officials met last week with hospital executives from across the state, who pitched a plan that the state adopted this week, distributing its most recent allocation of 342 courses of Paxlovid among hospital outpatient pharmacies.

Dr. Joseph Kanter, Louisiana’s top health official, said the idea was to ease the strain on overflowing emergency departments and intensive care units, allowing physicians in such settings to discharge at-risk patients after prescribing them the pill.

That will shorten the time between when a patient is identified as a candidate for Paxlovid and when the patient starts taking it, Dr. Kanter said.

“You have to put it in the hands of providers and pharmacists and provide the best guidance you can,” he said, “then step back and hope it gets to people who most need it.”