One of every five New York City residents tested positive for antibodies to the coronavirus, according to preliminary results described by Gov. Andrew M. Cuomo on Thursday that suggested that the virus had spread far more widely than known.

If the pattern holds, the results from random testing of 3,000 people raised the tantalizing prospect that many New Yorkers — as many as 2.7 million, the governor said — who never knew they had been infected had already encountered the virus, and survived. Mr. Cuomo also said that such wide infection might mean that the death rate was far lower than believed.

While the reliability of some early antibody tests has been widely questioned, researchers in New York have worked in recent weeks to develop and validate their own antibody tests, with federal approval. State officials believe that accurate antibody testing is seen as a critical tool to help determine when and how to begin restarting the economy, and sending people back to work.

“The testing also can tell you the infection rate in the population — where it’s higher, where it’s lower — to inform you on a reopening strategy,” Mr. Cuomo said. “Then when you start reopening, you can watch that infection rate to see if it’s going up and if it’s going up, slow down.”

The testing in New York is among several efforts by public health officials around the country to determine how many people may have been already exposed to the virus, beyond those who have tested positive. The results appear to conform with earlier research that indicated that the coronavirus began to circulate in the New York area by mid-February and came from Europe.

In California, two separate studies using antibody testing found rates of exposure as high as 4 percent in Santa Clara County and 5 percent in Los Angeles County — higher than those indicated by infection tests, though not nearly as high as found in New York. In Chelsea, Mass., public health researchers found antibodies in nearly a third of the 200 people tested.

In New York City, about 21 percent tested positive for coronavirus antibodies during the state survey. The rate was about 17 percent on Long Island, nearly 12 percent in Westchester and Rockland Counties and less than 4 percent in the rest of the state.

State researchers sampled blood from the approximately 3,000 people they had tested over two days, including about 1,300 in New York City, at grocery and big-box stores. The results were sent to the state’s Wadsworth facility in Albany, a respected public health lab.

Dr. Howard A. Zucker, the state health commissioner, said the lab had set a high bar for determining positive results, that it had been given blanket approval to develop coronavirus tests by the Food and Drug Administration and that state officials discussed this particular antibody test with the agency.

He said that while concerns about some tests on the market were valid, the state’s test was reliable enough to determine immunity — and, possibly, send people back to the office.

“It is a way to say this person had the disease and they can go back into the work force,” Dr. Zucker said. “A strong test like we have can tell you that you have antibodies.”

But he cautioned that the length of any such immunity remained unknown. “The amount of time, we need to see. We don’t know that yet,” he said, adding, “They will last a while.”

Unlike so-called diagnostic tests, which determine whether someone is infected, often using nasal swabs, blood tests for Covid-19 antibodies are intended to reveal whether a person was previously exposed and has developed an immune response. Some tests also measure the amount of antibodies present.

Hours before Mr. Cuomo’s presentation, a top health official in New York City expressed general skeptical about the utility of antibody tests — especially those on the private market — when it comes to questions of immunity and critical decisions over social distancing and reopening the economy.

Dr. Demetre C. Daskalakis, the city’s top official for disease control, wrote in an email alert on Wednesday that such tests “may produce false negative or false positive results,” pointing to “significant voids” in using the science to pinpoint immunity.

The alert, sent to medical providers and other subscribers, went on to warn that the consequences of relying on potentially false results may lead to “providing patients incorrect guidance on preventive interventions like physical distancing or protective equipment.”

Dr. Daskalakis, early in the outbreak, had been a strong voice arguing for social distancing measures and urging Mayor Bill de Blasio to close schools in New York City. When Mr. de Blasio resisted doing so, Dr. Daskalakis threatened to resign, a city official said. City Hall has said the mayor was never told of the threat.

Patrick Gallahue, a spokesman for the city health department, said the alert referred to private sector tests and not those conducted by labs like Wadsworth.

He added that there “isn’t any daylight here” between the city and state.

Dr. Michael Osterholm, an infectious disease expert at the University of Minnesota, praised the overall intent of New York’s study, but said the results in this case probably skew to a higher estimate than is real because a survey of grocery store shoppers in a pandemic would not be representative.

The sampling may disproportionately include those who have either already had the illness, or those who naturally tend to go out more and so are more likely to be exposed to the virus, he said. It would miss children, teenagers and older adults who may be sheltering in place.

“It’s not a criticism. It’s more of a comment that we have to be careful about interpreting supermarket customers as a representative sample when the state was in lockdown,” he said.

State officials said the test had been calibrated to err on the side of producing false negatives — to miss some who may have antibodies — rather than false positives, which would suggest a person had coronavirus antibodies when they did not.

Health experts have worried that if tests return high rates of false positives, they could encourage people to abandon protective measures and risk worsening the virus’s spread. Others warn that the true value of coronavirus antibodies is still unknown.

The World Health Organization, a United Nations agency, recommends that antibody testing be used only in research settings, and not to make medical decisions such as to permit an individual to return to work. States and the federal government are not bound by the organization’s advice.

“I’m very ambivalent about these tests, because we don’t really know yet through the science what it means to have an antibody,” said Dr. Joan Cangiarella, the vice-chair of clinical operations at N.Y.U. Langone Health’s pathology department.

“We are hoping these antibodies mean you will be immune for some time,” she said. “But I don’t think the data is fully out there to understand if that means that you’re actually immune. And if these antibodies start to decline, what’s that time frame? Does it decline in a year from now?”

Mr. Cuomo on Thursday did not talk about any potential for immunity among those previously infected.

But he did suggest, based on the survey, that if as many as 2.7 million New Yorkers had the virus, the death rate in New York from Covid-19 would most likely be far lower than previously believed, possibly 0.5 percent of those infected.

More than 15,000 people have died of the virus in the state, a figure that does not include an additional 5,000 people in New York City who were never tested but were presumed to have died from the disease.

The number of deaths has been increasing less quickly, and new hospital admissions for the coronavirus have remained relatively flat over the past three days: about 1,350 patients per day, down from over 2,000 per day last week. More than 263,000 have tested positive for infection.

Mr. Cuomo said antibody testing results, along with hospitalization numbers, would influence the state’s reopening strategy, noting that the number of people being hospitalized was still too high to consider easing restrictions.

The state’s plan would involve tracking infections as restrictions are loosened on gatherings and businesses. Antibody testing would be used, Mr. Cuomo said, for identifying coronavirus survivors who can donate convalescent plasma — the part of the blood that contains antibodies. Doctors at the Mount Sinai Health System in New York and elsewhere have been testing this use of plasma for treating patients with the virus.

After the city’s alert appeared on Wednesday night, the Greater New York Hospital Association, a powerful group with close ties to the governor, sent its own message to its member hospitals, suggesting that the city’s warning was overblown and highlighting how it differed from the state Health Department’s approach.

Susan C. Waltman, the association’s general counsel, said the tests are valuable for the information they can provide about the virus, and contrasted the city’s “absolute, rather dismissive terms” with what she described as an approach from the state that “tries to put the test results in perspective.”

Last week, Ms. Waltman, state health officials, and a group of senior doctors from 10 major academic and medical institutions across the state submitted a report to state health officials about how to roll out antibody testing.

The discussions were led by Dr. James Crawford, Northwell Health’s senior vice president for laboratory services. Dr. Crawford said in an interview that as of this week, the state’s major medical institutions estimated that they could perform between 5,000 and 10,000 antibody tests per day. They expect to increase that number significantly in the coming weeks and months, he said.

Dr. Crawford said there was a “pressing need to have both parts of the equation — who has the virus and who has mounted an immune response,” but he cautioned against using antibody testing as a criterion to allow people into the world.

“To use it as a fulcrum for when someone can travel or work,” he said, “I think we have to be extremely careful as a society in doing that.”

Reporting was contributed by Luis Ferré-Sadurní, Apoorva Mandavilli, Jesse McKinley and Donald G. McNeil Jr.