The Trump administration plans to adopt a decades-old testing strategy that will vastly increase the number of coronavirus tests performed in the United States and permit widespread tracking of the virus as it surges across the country.

The method, called pooled testing, signals a paradigm shift. Instead of carefully rationing tests to only those with symptoms, pooled testing would enable frequent surveillance of asymptomatic people. Mass identification of coronavirus infections could hasten the reopening of schools, offices and factories.

“We’re in intensive discussions about how we’re going to do it,” Dr. Anthony S. Fauci, the country’s leading infectious disease expert, said in an interview. “We hope to get this off the ground as soon as possible.”

In a call with reporters on Wednesday, Adm. Brett Giroir, deputy secretary of health and human services, said he expected the program to be up and running by the end of the summer.

“My assessment is that the data is very strong,” he said. By the time students return to universities, “pooling will be very mature.”

Given the many advantages, experts said, health officials should have embraced pooled testing much sooner. The United States military has used the technique at its bases worldwide, and has done so since it first tested men for syphilis in the 1940s.

Health officials in China, Germany, Israel and Thailand have all deployed pooled testing for the coronavirus. In Nebraska, a state scientist found a loophole that allowed him to circumvent federal prohibitions on the method. In Memphis, Dr. Manoj Jain, an infectious disease expert familiar with low-cost methods in India, has forged an ambitious plan to use the strategy.

“I’m just wondering why the federal government does not mandate now that this be done to preserve the testing capacity,” said Dr. Jain, of Emory University. “We really haven’t learned from our counterparts in Europe and Asia.”

Here’s how the technique works: A university, for example, takes samples from every one of its thousands of students by nasal swab, or perhaps saliva. Setting aside part of each individual’s sample, the lab combines the rest into a batch holding five to 10 samples each.

The pooled sample is tested for coronavirus infection. Barring an unexpected outbreak, just 1 percent or 2 percent of the students are likely to be infected, so the overwhelming majority of pools are likely to test negative.

But if a pool yields a positive result, the lab would retest the reserved parts of each individual sample that went into the pool, pinpointing the infected student. The strategy could be employed for as little as $ 3 per person per day, according an estimate from economists at the University of California, Berkeley.

By testing large numbers of people at a fraction of the cost, time and necessary ingredients, pooled surveillance could be widely adopted by workplaces, religious organizations, and schools and universities seeking to reopen.

The method works best in such settings, where the number infected is likely to be low, rather than in high-risk workplaces like meatpacking plants.

The technique was used to process tests for H.I.V. as that epidemic took root in the United States, recalled Dr. Fauci, who said he had been recommending it to federal officials for months. “Right now, there clearly is a very open, sympathetic ear to this,” he said.

Asked why the administration’s stance has changed now, Dr. Fauci referred to the alarming rise in infections nationwide. “Obviously, things are not going in the right direction,” he said.

In the absence of federal guidance, some health officials have forged ahead on their own.

In mid-March, as the number of infections in Nebraska climbed, the state was running out of supplies needed for coronavirus tests. The state lab had for years screened pooled samples of donated blood for pathogens and from pregnant women for sexually transmitted diseases.

Peter Iwen, the lab’s director, estimated that pooling coronavirus samples could conserve supplies and increase testing capacity by at least 70 percent. He tried to persuade officials at the Centers for Disease Control and Prevention to allow its assay to be used for pooled testing.

“They told me it’s an interesting concept, that’s as far as it went,” he said.

Dr. Iwen also appealed to the Food and Drug Administration. Officials said the agency could not comment on pending applications for emergency use authorizations.

But Gov. Pete Ricketts of Nebraska had declared a state of emergency on March 13, which meant that certain federal and state rules could be superseded. With permission from the governor, Dr. Iwen moved to put pooled testing in place.

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Looking for ideas to contain a coming surge in coronavirus infections, Mayor Jim Strickland of Memphis called Dr. Jain, who recalled a World Health Organization mission to India in November where he had seen pooled testing for tuberculosis.

Dr. Jain, like Dr. Iwen, found that in the federal government, “there was no one really encouraging this to be done.” But he proceeded with the mayor’s blessing. Hundreds of Memphis firefighters, police officers and city workers volunteered to swab their own noses.

The lab tested the samples in batches of three, five, seven or 10, and determined that pooling seemed to work best with batches of seven. The data were submitted to the F.D.A.; the agency has responded positively, but has not yet authorized the pooled method, Dr. Jain said.

Pooled surveillance has its limitations. The savings in time and expense thin out when the number of infected people rises above 10 per 100. Because so many pools then are likely to yield positive results, laboratories wind up testing huge numbers of individual samples.

Nebraska, for example, suspended its program about a month ago when meatpacking plants in the state exploded with coronavirus infections and the rate of positive samples arriving at the lab spiked above 10 percent.

The technique also loses accuracy beyond that range. Dr. Jain said that weakness was not a pressing concern, because pooled testing’s main goal is to identify people who have a high viral load and could transmit the virus, not simply to find every infected person.

“This is not a diagnostic test, but a screening test,” he said. “The bar can be much lower for a screening test.”

The F.D.A. has released guidelines for developers to adapt their tests to pooled samples. The agency is also asking manufacturers to permit labs to use the tests without being explicitly authorized by the F.D.A. to do so.

“If the F.D.A. is able to do this, I think it would be a big deal for the U.S.,” Dr. Iwen said.

Federal law forbids any lab without the right credentials from conducting diagnostic tests and revealing the results to patients. But on June 19, the Centers for Medicare and Medicaid Services, which oversees lab testing, said it did not consider pooled surveillance to be diagnostic — meaning any private or academic lab can screen and reveal the grouped results from a pool to the set of patients who contributed samples.

But if a batch tests positive, the retesting of each patient’s sample would be considered a diagnosis and need to come from a certified lab — tacking on a delay of several days for the verdict — noted Kelly Wroblewski, chief of infectious diseases at the Association of Public Health Laboratories.

“That’s where I think we probably start to disagree with pooling as a strategy,” Ms. Wroblewski said. The F.D.A. and C.M.S. have always required screening tests to be done at a certified lab, so the change in policy needs further discussion, she said.

She added that pooling was also unlikely to be useful at most state labs, which now tend to see samples from at least 15 infected people for every 100, well above the recommended cutoff of 10 percent. “I don’t think it’s going to solve all our problems,” she said.

Dr. Thomas R. Frieden, a former director of the C.D.C., warned that any testing strategy was unlikely to succeed without isolation of those tested until results are available, and reasonable options for isolating away from the home for anyone who is found to be infected.

“What I find both frustrating and dangerous is the consistent failure to understand that testing, in and of itself, pooled or not, does little or no good,” Dr. Frieden said in a email.

“What good is testing if the results take four days to come back and infectious people aren’t isolated in the interim? What good is testing if contact tracing doesn’t identify and warn exposed people quickly?”

Dr. Fauci acknowledged that the country was not adequately isolating people. But, he added, above a certain level of infection, “the core paradigm of identification, isolation and contact tracing just doesn’t work.”

Faced with rising cases in multiple states, he said, the administration is consulting with statisticians to estimate the ideal proportions for a pool in a particular location.

In the meantime, more states have come around to the idea. Dr. Iwen said that in the past three weeks, about a dozen state lab directors had contacted him to ask about Nebraska’s experience.

Even in states like Arizona, where the percentage of positive tests may exceed 20 percent, pooled testing could be used in settings such as schools where the prevalence is likely to be much lower, he said — especially as the shortage of testing supplies continues to be a problem.

“We’re being asked to expand surveillance testing to large populations of people, and there quite frankly is not enough reagents to be able to do that,” he said, referring to chemicals used in diagnostic tests. “It’s becoming a national discussion now.”