He singled out Florida, whose case rate continues to increase.
"Florida has a serious problem with the number of ICU beds that are being occupied," Cuomo said during a conference call.
Hours later, Florida Governor Ron DeSantis was asked about the possibility that residents of his state will be asked to quarantine upon arrival in New York.
"Well I think governors have prerogative to do what they need to do. I would just ask if that's done just please do not quarantine any Floridians in the nursing homes in New York."
At his telephone news briefing Saturday, Cuomo said he is keeping a close eye on other states with high infection rates.
"We're also watching how many people are actually coming to New York from those states," Cuomo said.
Florida reported 4,049 new cases of COVID-19 on Saturday, marking three straight days of record-breaking numbers. The state is now now up to 93,797 total confirmed cases and 3,144 deaths associated with COVID-19, according to the latest data released by the health department.
The governor said he will act accordingly if a large number of people start to make their way toward New York.
"So if we start to see a large influx of people coming from one of the states that has a high transmission rate, that would be a cause for concern," he said. "And we're watching it day to day there's no deadline on it. You know, we're reacting to the facts as they develop."
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