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ALBANY — New York state has 2,959 positive coronavirus cases, a surge in diagnoses after health officials performed 8,000 tests for the disease overnight, Gov. Andrew Cuomo said Thursday.

The tally is nearly 500 more than a day ago — showing the urgent need for help from the feds, Cuomo said.

“This is a crisis for our health care system management, it’s the capacity for our health care system. Do we have enough beds? Do we have enough gloves? Do we have enough PPE [personal protective equipment]? And the answer is no, that’s why the federal government is now fully engaging,” the governor said Thursday morning on CNN.

“This is going to be the matter of life and death for people. We now have about 5,000, 6,000 ventilators in New York state. We’re going to need about 30,000 ventilators because these people who come in all have respiratory illnesses,” Cuomo added.

New York City alone has an estimated 3,500 machines, a spokeswoman for Mayor Bill de Blasio said.

“You can’t buy a ventilator right now … you’re going to have to make them, or make something like them,” said Cuomo, who is urging the feds to order mass manufacturing of the hard-to-come-by machines.

Meanwhile, Cuomo continued to rail against against officials — chiefly de Blasio — who are floating the idea that the Big Apple will adopt a “shelter-in-place” lockdown model akin to San Francisco.

The debate has placed the governor and mayor at odds, and de Blasio appeared to back down from calls Wednesday following a phone call with Cuomo.

“Look at your words, ‘shelter-in-place,’ you know where that came from? That came from nuclear war. What it said is people should go into an interior room of their home with no windows, stay there until they get the all clear sign. Now, that’s not what people really mean, but that’s what it sounds like,” the governor seethed.

He has said he would prefer a statewide lockdown, and possibly a multi-state effort including New Jersey, Connecticut and Pennsylvania.

“People stay home. Reduce density. Close businesses. But you’re not imprisoned. You’re not quarantined. You’re not a prisoner. We’re not going to put a roadblock around New York City so you have to pack up and get out today. This is going to go on for months.”

“Communicate what you mean without using terms that nobody understands and only incites panic, because that’s what we’re doing in too many situations.

“You can communicate what you want, but just say it in a more clear way, rather than using these buzzwords that are panicking people. I am not going to imprison anyone in the state of New York. I am not going to do martial law in the state of New York. That’s not going to happen,” he said.