The number of positive cases of coronavirus in New York climbed to 328 on Thursday, but Gov. Andrew Cuomo said he would not be surprised if that number was more than 3,000, stressing that there is no way to know the breadth of the virus because the state lacks adequate testing supplies.

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"We are way behind in testing determining how many people are actually infected," Cuomo said at a news conference.

The governor said there are 28 labs in New York state that have conducted coronavirus tests on 2,314 people. At least 2,000 people have been quarantined statewide in an effort to slow the spread of the virus.

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"The more people you test the more people you can isolate," he said, adding that New York doesn't "have the testing capacity to actually determine" the percentage of the population that has coronavirus.

Cuomo said that the state is attempting to contract with a national lab to increase the number of tests they can perform, and he predicted that number could climb to up to 5,000 by next week if the Food and Drug Administration (FDA) approves the partnership.

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In all, 47 people diagnosed with the virus have been hospitalized -- about 14 percent of the cases statewide.

"This is evolving situation numbers and facts change evry day," Cuomo said.

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As the virus ramps up, Cuomo also banned all gatherings of more than 500 people and placed unprecedented restrictions on Broadway productions to limit audiences and ramp down on person-to-person interactions in an effort to control the spread of the virus.