Trump administration officials announced Tuesday that they had begun high-volume coronavirus testing in three communities temporarily in an experiment to try to tamp down rising numbers of cases and hospitalizations.

In what Department of Health and Human Services officials are calling surge testing, the government is sending in contractors and arranging laboratory services to provide 5,000 diagnostic tests per day each in Baton Rouge, La.; Edinburg, Tex.; and Jacksonville, Fla. The sites will last five to 12 days in each place unless state officials want to keep them going. People will not be charged for the tests.

The project, coming as testing capacity is being strained by an upswing of coronavirus cases in 30 states, is focused in particular on ferreting out cases among relatively young adults who may not have symptoms and may be unaware they are spreading the potentially deadly virus.

“We can’t test our way out of this,” Brett P. Giroir, an HHS assistant secretary who is the administration’s coronavirus testing coordinator, said of the nation’s recent run of record new cases. But identifying unwitting spreaders, he said, can prompt those people to isolate themselves and increase awareness of the importance of wearing masks, keeping safe distances, washing hands and protecting the elderly or those who have other vulnerabilities that put them at risk for serious illness or death if they become infected.

He dispatched what he called his “highly proselytizing” message about following safety guidelines as the number of confirmed U.S. cases  approaches 3 million. Nationwide, at least 128,000 have died of covid-19, the disease caused by the virus.

Giroir said the three communities were selected from a list of 10 locations developed by Deborah Birx, the White House’s coronavirus response coordinator. The list contains medium-size metropolitan areas with worsening outbreaks and a well-developed state or local capability to perform coronavirus testing, he said.

“Don’t get the impression they are the bottom of the barrel,” Giroir said during a conference call with journalists.

Jacksonville also is the site late next month of most of the Republican National Convention, where President Trump is expected to be nominated formally as the GOP presidential candidate for the November elections. The event was shifted there a few weeks ago from Charlotte after North Carolina’s governor refused, because of the pandemic, to guarantee that convention-goers could fill the original arena.

Asked whether the convention was a factor in Jacksonville’s inclusion in the surge testing sites, Giroir replied, “I had no idea the Republican convention was even in Jacksonville until I called the state health officer and he told me. That shows you where my mind is . . . It makes no difference to me what’s going on in any town. It just met the public health criteria.”

Four surge testing sites opened Tuesday in Baton Rouge, according to HHS. One site in Edinburg and three in Jacksonville are scheduled to start Wednesday.

According to Washington Post data, Duval County, with Jacksonville as its county seat, has more than 9,800 coronavirus cases, the sixth-highest total in Florida. As of Tuesday, it had a seven-day average of 518 new daily coronavirus cases, compared with 21 a month ago.

Hidalgo County, Tex., where Edinburg is the county seat, has more than 5,300 cases, the state’s seventh-highest total. It has a seven-day average of 293 new daily cases, compared with 20 a month ago.

Baton Rouge is split between two Louisiana parishes. One of them, East Baton Rouge, has that state’s third-highest number of cases — about 6,200. And its seven-day average of new cases — 253 as of Tuesday — is essentially unchanged from a month ago.

Giroir said federal officials might expand the surge testing to other sites on Birx’s list — or potentially add to that list — but first wanted to assess whether the testing surge in the initial three communities reduced the virus’s spread.

He said the number of diagnostic tests performed nationwide had peaked at more than 700,000 one day last week and has been averaging around 600,000. New cases are reaching record levels many days, in large part based on huge outbreaks in California, Arizona, Texas and Florida.

Those record case numbers are causing testing in parts of the country to near its capacity. Giroir said that the nation’s large diagnostic laboratories have not exceeded the number of tests they can run but added that “we are certainly pushing the frontiers.”

One consequence is longer wait times for people to get their test results. He said just two places, Montana and the District of Columbia, have average wait times of four to five days for results to come back. The rest of the states have shorter average waits.

Despite some complaints of shortages of testing materials, Giroir said that “states are getting all the upstream supplies they are asking for,” though some may not always get the specific reagents they request.

Under the surge project, laboratories have promised to turn around results within 48 hours of receiving specimens, so people who get tested might encounter overall waits of three or four days from the time of their test.

The federal surge project began a few days after reports of people waiting in long lines of cars to get coronavirus tests, especially across the South and Southwest. At one free testing event last month in Phoenix, more than 1,000 cars — hundreds more than expected — waited in lines that lasted miles, and the whole thing lasted seven hours longer than scheduled.

In Austin, public health officials had widened their rules to test anyone wanting to find out whether they had been infected but ended up being so overwhelmed that they reverted to providing tests only to people with suspicious symptoms or at higher risk of poor outcomes if they were to be infected.

Jacqueline Dupree contributed to this report.