New York Governor Andrew Cuomo speaks during a press conference to discuss the novel coronavirus or COVID-19 in New York State on March 2, 2020 in New York City.

Gov. Andrew Cuomo identified New Rochelle, a city in Westchester County where the second confirmed coronavirus patient in the state was found, as a "significant hot spot" in New York, which now has at least 142 confirmed cases.

Cuomo said he's been in talks with officials from the Centers for Disease Control and Prevention about the outbreak in New York, particularly in New Rochelle.

"Westchester is our problem," Cuomo said. "That is a relatively small community in New Rochelle with 98 cases, more than the city of New York."

He said 19 cases have been confirmed in New York City and 17 cases in Nassau County, as of Monday morning.

Schools might be closed "for a number of weeks" in the New Rochelle area, he said, and going forward, if a student tests positive, their school will be closed "for an initial 24-hour period" while officials investigate.

"We have closed the [New Rochelle] schools now. The question will be duration. We could be talking weeks," Cuomo said.

The Department of Health will "issue a joint regulation today saying if a child tests positive in a school, that school is closed for 24 hours to assess the facts and circumstances of that school and determine what should be done going forward," Cuomo added when pressed on the details of the 24-hour closure.

Cuomo's remarks come just days after he declared a state of emergency in New York, as the coronavirus becomes more severe in the state.

On Monday, Cuomo and New York Mayor Bill de Blasio urged people to avoid dense crowds, particularly while using mass transit. During the press briefing, Cuomo confirmed that Rick Cotton, the executive director of the Port Authority of New York and New Jersey, has tested positive for the new coronavirus and will be "on quarantine."

The New York governor also addressed price gouging ahead of his remarks about school closures, unveiling during the briefing a hand sanitizer he said was created and distributed by the New York state government.

"To Purell and Mr. Amazon and Mr. eBay, if you continue the price gouging, we will introduce our product, which is superior to your product," he said, in apparent jabs to hand sanitizer company Purell, Amazon CEO Jeff Bezos and eBay CEO Scott Schenkel.

The coronavirus, which is believed to have originated in Wuhan, a city in China's Hubei province, in December, has spread to dozens of countries globally with more than 111,000 confirmed cases worldwide and at least 3,892 deaths so far, according to data from Johns Hopkins University.

There have been at least 566 cases in the United States and at least 22 deaths, according to Johns Hopkins.

The outbreak has roiled markets and led governments to take drastic actions as it rapidly spreads across the globe.

Clarification: This story was updated to reflect that the New Rochelle patient was the second confirmed coronavirus case in New York state. He was the first confirmed case that wasn't travel related.