NEW YORK — More evidence is emerging that far more New Yorkers have had the coronavirus than the number confirmed by lab tests, officials said Thursday.

A state survey of around 3,000 people found that 13.9% had antibodies suggesting they had been exposed to the virus, Gov. Andrew Cuomo said at his daily news briefing in Albany.

In New York City, 21% of the people tested had antibodies.

Cuomo cautioned that the data was preliminary. The sample of people tested was small and people were recruited for the study at shopping centers and grocery stores, which meant they were healthy enough to be out in public.

Experts also say having antibodies is not necessarily proof someone is immune from the virus.

But Cuomo said knowing how many people have antibodies could potentially help set policy on when to reopen parts of the state.

More than 263,000 statewide have tested positive for the virus.

Earlier Thursday, New York City’s health commissioner said many as 1 million people in New York City may have been exposed to the coronavirus.

More than 142,000 people in the city have tested positive for the virus, “but that really is, I think, the tip of the iceberg,” Dr. Oxiris Barbot said.

She noted the city is still telling people who suspect they have the virus but aren’t seriously ill that they don’t need to seek a test, so the true number of sick people is unknown.

“It wouldn’t surprise me if, at this point in time, we have probably close to 1 million New Yorkers who have been exposed to COVID-19,” she said.

Early on in the pandemic, health officials estimated that as many as half of all people in the city would get the virus. Mayor Bill de Blasio said that’s still plausible, though the lack of comprehensive, widespread testing makes it difficult to say for sure.

“We are still dealing with the great unknown in the absence of testing. We don’t even 100 percent know when the first cases emerged in this city, because we didn’t have testing in February. We know it was February, but we don’t know how many people got it back then.”

Blood tests that check for antibodies, substances the immune system makes to fight the virus, are expected to allow health officials to better understand how many people had the virus with few or no symptoms.

But such tests need to be done with random sampling, ensuring that the people being tested are representative of the geographic, social, racial and other conditions. There are also questions about the accuracy of the blood tests being used. Scientists have found that some of them aren’t reliable enough, with too many false positives and false negatives.

De Blasio said that “in a perfect world” hundreds of thousands of people a day would be tested for the coronavirus in the city.

He said the city needs help from the federal government to reach that level of testing but is building testing capacity and should reach 20,000 to 30,000 tests a day by next month.