A small commercial laboratory in Georgia has been selling do-it-yourself coronavirus testing kits, despite the fact that the Food and Drug Administration has not approved at-home testing for people worried they may have been infected in the global pandemic.

A physician at the health clinic working with the Georgia lab said there is no time to waste on federal bureaucracy.

“We’re behind the eight ball. We need to start testing more people,” said David Williams, the chief executive of Southside Medical Center in Atlanta. “It doesn’t bother me that they haven’t given approval, because that doesn’t mean it doesn’t work. That doesn’t mean the test is not accurate.”

The situation is an illustration of the growing desperation among Americans for confirmation about whether they have been sickened by a virus that has spread to all 50 states, resulting in more than 5,800 cases nationwide, according to researchers at Johns Hopkins University, and 100 deaths, according to a Washington Post analysis.

The push to accelerate coronavirus testing nationwide made significant advances this week, from the Pacific Northwest to the Northeast. On Tuesday, Adm. Brett Giroir said that nearly 59,000 tests had been done, with commercial labs administering 8,200 on Monday alone. A handful of drive-through testing operations have been set up in large and small cities: Giroir said 47 would start up in a dozen states “over the next few days.”

But the United States still lags behind other countries, and the apparent demand for at-home testing shows that government and industry officials are still struggling to launch widespread testing needed to curb the pandemic’s spread and change its outcome.

With all 50 states tackling the pandemic in varying ways, Americans are experiencing uneven access to care.

“If you get large-scale testing such that everyone could do it, we could have a much better sense of the scale of the problem,” said William Hanage, an epidemiologist at the Harvard T.H. Chan School of Public Health.

LifeHope Labs, which began selling the at-home kits last week, had processed about 100 tests by Friday and more than 300 as of Tuesday afternoon, according to Tim Allen, the chief operating officer. Initially, the company charged $240 per test. Now, the price has dropped to $150, including shipping and handling. LifeHope is equipped to handle 846 samples a day and is ramping up to double that number this week.

“For people who want to get tested, we just want to be able to give them a way to get tested,” said Allen, whose lab is federally certified and has been running the coronavirus test developed by the Centers for Disease Control and Prevention.

After Georgia officials warned that such direct-to-consumer testing was not allowed, Allen said, LifeHope partnered with physicians who can order the tests to be mailed after a telemedicine appointment — still without FDA approval. LifeHope ships kits overnight to people who swab their own noses with a long cotton swab and then ship the sample back to LifeHope on ice.

Tom Inglesby, director of the Center for Health Security of the Johns Hopkins Bloomberg School of Public Health, said such nasal swabs can be uncomfortable and difficult for an untrained person to perform effectively, raising the risk of false negative results. “It’s more complicated than spitting in a cup,” he said.

Another company — Zymo Research of Irvine, Calif. — has also developed an at-home kit that it hopes to get into the hands of first-responders and companies so that they can test employees. The kit contains a pair of latex gloves, a cotton swab for collecting a sample from the back of the throat and a liquid medium in a plastic tube to preserve the sample.

Zymo acts as a middleman, passing the sample to Pangea Laboratory in Costa Mesa, Calif., said Marc Van Eden, vice president of business development at Zymo Research. The lab can process results in 24 hours, he said, but is waiting for FDA approval before going to market.

With access to traditional testing still limited, the Trump administration has said priority will be given to health-care workers and people older than 65, who are at higher risk for complications.

On the ground floor of a parking garage at the University of Washington Medical Center-Northwest on Monday, cars moved at a measured clip as four nurses wearing scrubs, gloves, surgical masks, and clear plastic eye shields tested health-care workers for covid-19, the disease caused by the coronavirus. Traffic cones marked the site, which was flanked by three white tents, biohazard disposal bins, a hand-washing station and heat lamps that warmed up the chilly garage.

Alex Greninger, assistant director of the virology division at the UW Medical Center in Seattle, said his lab has enough capacity to test about 1,800 people per day. But having received more than 2,300 specimens in one day last week, he has had to figure out how to triage.

“We are communicating with our clients — people who send tests to us — to prioritize inpatients, first responders, health-care workers, vulnerable populations,” he said in a phone interview, adding that they do not want requests from outside the hospital to delay tests for patients. “That is the real worry here.”

In the District of Columbia, George Washington University Medical Faculty Associates is limiting nearly all of its tests to patients with obvious symptoms consistent with the virus to conserve the limited supply of kits and protective gear.

“We would like to be able to test as many people as possible,” said William Borden, the group’s chief quality and population health officer. “Right now we have several hundred test kits. We’re trying to be judicious, that we’re using them for people who have a high likelihood of being positive.”

Ryan Westergaard, chief medical officer for Wisconsin’s Bureau of Communicable Diseases, told reporters on Monday that state officials are optimistic they will expand their testing capacity but are not there yet.

The state public health lab, where most coronavirus testing is taking place, has been running seven days a week and currently can process about 400 tests per day. He estimated that a handful of other hospitals and private labs in the state, which had 46 active cases of the coronavirus as of Monday, can collectively test up to another several hundred prospective cases a day.

“At the present moment, there’s not enough capacity to test every person — or even every person with respiratory symptoms,” Westergaard said.

The FDA announced Monday that states could approve tests developed in laboratories in their states without getting the agency’s authorization in an effort to speed development.

But even as major lab supply firms are ramping up production and the Trump administration says the effort will scale up quickly, laboratories are constrained by limitations.

Thermo Fisher Scientific, a lab supply giant, has 1.5 million tests ready to ship this week and expects to increase quickly to 2 million tests per week. But hospital labs still need time to set up a process for administering them. Thermo Fisher spokesman Ron O’Brien, whose company is initially distributing its tests to 200 labs in the United States, said that could take a few days to a week.

The tests must run on a specific laboratory instrument, which can process up to 846 tests per machine per day if it is testing around the clock. Thermo Fisher hopes to be able to ship 5 million tests per week by April, but it will depend on the availability of raw materials, including reagents used to extract the genetic material from samples.

Roche, a pharmaceutical giant, can supply about 3.5 million tests per month, but these tests also must run on specific instruments in limited supply. There are fewer than 830 of these machines across the globe.

As testing ramps up, some laboratory industry officials are worried about a shortage of supplies, such as the swabs health-care workers use to collect samples from patients. Carmen Wiley, president of the American Association for Clinical Chemistry, said that the FDA requires swabs made by a single manufacturer and that some labs are running low. Wiley also said there remains a shortage of RNA extraction kits, which are used by laboratories to extract the virus’s genetic material from the swabs.

An FDA official said the agency has provided additional flexibility in using both kinds of supplies, but some industry officials say even those looser requirements won’t solve the problem.

The shortage of testing kits from the federal government has triggered a race to come up with new techniques to detect the coronavirus. More than 60 researchers at Yale University and a nearby private firm called Homodeus are developing a test that people could administer at home, similar to a home pregnancy test.

“So you can spit into a tube. And get results. No lab. No technician. No expensive machines. No wait,” said Jonathan Rothberg, an entrepreneur and genetics researcher leading a team at the Yale School of Medicine. Results would be available within half an hour.

But Rothberg, who noted that the Bill and Melinda Gates Foundation is also working on a mail-in kit, said even his group’s high-speed efforts would only be scaled up if they were clinically validated.

On Tuesday, White House Coronavirus Response Coordinator Deborah Birx said experts were exploring “innovative solutions,” like self-swabbing, but did not have enough data yet.

In some parts of the country, people are already getting better access to tests. Tony Dunn and his wife, both in their 60s, started showing symptoms last week and were initially unable to get tested because they had not traveled internationally nor been in contact with a confirmed case of the coronavirus. On Monday, their doctor told them that drive-through testing for the flu and the coronavirus had just opened near their home in Flat Rock, N.C.

They arrived an hour after the station opened to find 15 cars in line, Dunn said. Their coronavirus test results are due Friday. “Considering that we live in a small town in western North Carolina, I’m fairly impressed by how quickly they got their act together,” Dunn said.

Steven Mufson, Neena Satija, Brady Dennis, Shane Harris and Gregory Scruggs contributed to this report. Scruggs reported from Seattle.