The Biden administration’s new website allowing people to order up to four free at-home coronavirus tests quietly went live on Tuesday — a day in advance of its formal launch — and demand already appears to be significant.

There were more than 700,000 visitors on the home page of covidtests.gov, early Tuesday afternoon — more than 20 times higher than the government site with the next highest traffic, the U.S. Postal Service’s package-tracking page, according to https://analytics.usa.gov, which monitors traffic on participating federal government websites.

At a White House news conference on Tuesday, the press secretary Jen Psaki said the “official launch” was Wednesday morning, but that the site began taking orders during what she described as a “beta testing phase” being conducted by the U.S. Digital Service, the government’s technology support division. The Postal Service is handling the orders.

It wasn’t long before the pilot testing picked up an apparent glitch. A White House spokesman said the Postal Service would address an issue where some people living in apartment buildings reported being blocked from ordering their own tests, after tests had already been requested for the building’s address by other tenants.

President Biden has experience with fumbled website rollouts; when he was vice president, he and President Barack Obama presided over the disastrous launch of healthcare.gov, the online health insurance marketplace created by the Affordable Care Act. Jeff Zients, who is now Mr. Biden’s coronavirus response coordinator, was brought in to rescue the troubled site. The U.S. Digital Service was created in its aftermath.

Visitors to covidtests.gov can click through to a Postal Service webpage, where they can order up four tests per household, free of charge. Orders will usually ship in 7 to 12 days, the website says.

“We can’t guarantee there won’t be a bug or two,” Ms. Psaki said, “but the best tech teams across the administration and the Postal Service are working hard to make this a success.”

Matching testing supply with demand has been a persistent challenge for both the Trump and Biden administrations, and Mr. Biden has come under criticism for not ramping up the supply of rapid at-home tests quickly enough as Americans struggled to get tested amid the emergence of the highly contagious Omicron variant. The Biden administration has ordered a billion at-home tests to give out free to the public, in two 500-million tranches.