"I'm worried about nursing homes, senior care facilities," Cuomo said. "That is something we worry about. My own mother is elderly." People with compromised immune systems, cancer patients or HIV-positive people, should be more careful, he said.

At least eight of the new coronavirus cases are connected to a lawyer from Westchester, who was the second confirmed case in the state. Two of the new cases are in New York City and one is in Long Island, he said.

The number of COVID-19 cases in New York doubled overnight to 22 as the state ramps up its testing, Gov. Andrew Cuomo said Thursday, adding that four people have been hospitalized so far.

There are about two to three dozen people in the state who are under mandatory quarantine with roughly 1,000 additional people in self-quarantine. The state is currently testing between 100 and 200 people for COVID-19 every day, Cuomo said.

"The number will continue to go up," Cuomo told reporters at a news briefing. "It must because we are continuing to test."

The Westchester lawyer, who worked in Manhattan, is recovering at New York Presbyterian Hospital, New York Health Commissioner Dr. Howard Zucker said. The lawyer's infection, which was the second in the state, was confirmed on Tuesday. On Wednesday morning, Cuomo said his family and a neighbor all contracted the virus. Cuomo announced later that day that the lawyer also passed the virus on to a friend who passed it on to the rest of his family.

Cuomo tried the tamp down public anxiety, saying 80% of the people who become infected may not even know they have it, "just like the flu."

"Look at the stock market, right. It could have an affect on the national economy. It could have an impact on the global economy depending on how it's perceived," he said. "The numbers are going up. It's like the stock market going down everyday."

New York City Mayor Bill de Blasio confirmed the two cases in New York City earlier Thursday. He said the patients had no known connection to other people recently diagnosed with the virus or travel history to known sites of an outbreak. That indicates that the virus could be spreading undetected throughout the city.

CNBC's Noah Higgins-Dunn contributed to this article.