New York’s health commissioner on Monday defended a directive that requires nursing homes to readmit residents who’ve tested positive for the coronavirus — as Gov. Andrew Cuomo revealed he didn’t know the policy was in place.

Cuomo was asked about the state’s policy on admitting or readmitting to nursing homes people who’d tested positive for COVID-19.

“That’s a good question, I don’t know,” the governor said.

Cuomo’s startling admission came days after the state revealed last week that at least 3,316 people in nursing homes and adult care facilities had died of coronavirus at their residences or in hospitals across the state.

That tally — which officials have said is likely an undercount — included at least 2,056 deaths in New York City.

Updated statistics released Monday afternoon increased the death toll to 3,448 as of Sunday, with 2,105 in the Big Apple.

Health Commissioner Howard Zucker, to whom Cuomo referred the question, said that under the state’s policy, “if you are positive, you should be admitted back to a nursing home.”

“The necessary precautions will be taken to protect the other residents there,” he said during Cuomo’s daily coronavirus briefing in Albany.

Zucker was asked to explain how the policy could be justified, given how state officials have repeatedly said how quickly the virus can spread and how vulnerable nursing home residents are to COVID-19.

“And that’s why we’re working closely with the nursing home leadership and the individuals who are working in the nursing homes to protect those individuals who are coming back who have COVID-19 and went back to the nursing homes and where they came from,” he said.

Assemblyman Ron Kim (D-Queens) said Zucker’s assertion that “necessary precautions” were being taken to prevent the spread of infections in nursing homes was “clearly not the case.”

“It’s either he’s lying or they have absolutely no idea what’s going on on the ground,” Kim said.

“The staff, the families, everyone is telling me there’s completely a lack of support and they don’t have the necessary PPE [personal protective equipment] to be safe.”

The COVID-19 readmission policy was adopted March 25 and was contained in a Health Department directive that says, “No resident shall be denied readmission or admission to the [nursing home] solely based on a confirmed or suspected diagnosis of COVID-19,” Newsday reported last month.

At the time, the head of the New York State Health Facilities Association, which represents the nursing home industry, described the policy as unprecedented and said it raised “significant concerns for nursing homes that don’t have coronavirus-positive residents or are at capacity.”