WASHINGTON — Americans will be able to request free rapid coronavirus tests from the federal government beginning on Wednesday, but the tests will take seven to 12 days to arrive, senior Biden administration officials said on Friday.

The administration’s website to process the requests, covidtests.gov, was up and running on Friday, the latest sign of its efforts to ramp up access to testing since the fast-spreading Omicron variant sent coronavirus case counts soaring.

But the delay in accepting orders and the lag in shipping mean that people are unlikely to receive the free tests until the end of January at the earliest. In some parts of the country, that may be after the peak of the current surge of cases.

President Biden said last month that his administration would purchase 500 million rapid at-home coronavirus tests and distribute them to Americans free of charge. On Thursday, he announced plans to buy an additional 500 million tests, bringing the total to one billion. The administration has already contracted for 420 million tests.

Each household will be limited to four free tests. The Postal Service will handle shipping and delivery through first-class mail, the officials said. Free tests will also be available at some community health centers, rural clinics and federal testing sites.

Separately, people with private insurance should be able to start seeking reimbursement for tests they purchase themselves beginning on Saturday, less than a week after the administration announced the new rule. Insurers will be required to cover eight at-home tests per person per month.

The administration is also creating incentives to encourage insurers to work with pharmacies and other retailers so people can be reimbursed at the time of purchase, as is often the case with prescription drugs. But some insurers say it will probably take weeks to fully set up the system the White House envisions.

Expanding testing capacity is one of a series of steps the Biden administration has taken to step up its response to the Omicron variant, which arrived in the United States shortly after Thanksgiving and has pushed hospitals to the brink of being overwhelmed in at least two dozen states. On Thursday, Mr. Biden announced that he was sending military medical personnel to six states to bring relief to overwhelmed hospital workers.

The White House has faced harsh criticism for failing to have enough tests before the Omicron surge. Some public health experts have been calling for months for the government to make better use of coronavirus tests as a way to control the spread of the virus, and to create a guaranteed market for diagnostics by purchasing them directly from manufacturers.

One of those critics, Dr. Mara Aspinall, an expert in biomedical diagnostics at Arizona State University, called the president’s recent moves to expand testing “an important step forward,” and an essential acknowledgment of the importance of testing as a mitigation strategy.

“You’ve got to give them credit for getting this done in less than a month,” she said, while noting that the seven-to-12-day time frame “is not ideal.”

Testing has been a challenge for the federal government since the earliest days of the pandemic. Supply chain shortages made them hard to come by, and overloaded laboratories took days to process them. Mr. Biden, who came into office promising to ramp up testing, has made some progress in expanding the supply of rapid at-home tests. There were none available to American consumers when he took office.

But the Omicron wave has put intense pressure on the nation’s testing capacity. At-home tests began flying off pharmacy shelves and are now scarce in many parts of the country. At the same time, some consumers are confused about how to use them.

Administration officials sought to clear up some of that confusion on Friday, specifying three reasons people should use at-home tests: They begin to have symptoms of Covid-19; they were exposed to someone who tested positive for the virus five or more days earlier; or they are planning to gather indoors with someone at risk of Covid-19, and want to assure themselves they are negative.

Beyond limited availability, cost has been a major barrier in access to at-home tests. They are expensive: about $12 each, or $24 for a package of two.

The administration has pledged to ensure equitable distribution of the tests. A White House fact sheet said the government would place a high priority on getting tests to “households experiencing the highest social vulnerability and in communities that have experienced a disproportionate share of Covid-19 cases and deaths.”