The next tranche of tests should be available with a “pretty rapid turnaround,” he added.

Public health experts said the tests, however late they arrived, had important purposes beyond diagnosing infections. Lindsey Dawson, a policy analyst at the Kaiser Family Foundation who has studied rapid test availability, said the mail program had helped shift the perception of rapid tests from a scarce luxury to a normal, accessible resource.

“Just making somebody familiar, like, ‘Oh, this isn’t so intimidating. I can have these at home. I can use them for myself. I can use them on my child and move about the world in a way that feels more secure,’” she said of the mass distribution.

The Centers for Disease Control and Prevention still recommends using at-home tests after being exposed to the virus, when experiencing Covid symptoms, or before indoor gatherings with vulnerable people.

Other components of the Biden administration’s pandemic response will rely on testing, such as the “test to treat” initiative, which allows Americans to get tested at pharmacies, community health centers and long-term care facilities, and to receive antiviral drugs on the spot if they test positive.

Some public health experts, meanwhile, have warned that after the C.D.C. recently relaxed mask recommendations for much of the country, people might take more risks that could expose them to the virus, even when there is less of it around.

Millions of Americans have immune deficiencies, and the youngest children are still ineligible for vaccination.

Christina Rondinone, a stay-at-home mother in Jupiter, Fla., has maintained a small stockpile of tests in recent months, from a nearby pharmacy and the Postal Service program. She plans to order four more tests from the government, which she can use before visiting her father, who has lung and kidney disease and requires dialysis, putting him at risk of severe Covid. Ms. Rondinone, 35, said the tests were akin to a first-aid kit in her home; she would like to start using them after attending crowded indoor events without a mask, she added.