New York State has ramped up testing and now has 10,000 confirmed cases of the new coronavirus, Governor Andrew Cuomo said on Saturday.
The majority of the cases are in New York City, the most densely populated area.
Westchester, an initial epicentre, is seeing efforts to stem the spread succeeding in that town, just north of the city.
New York was now doing more testing than any other state in the country and was reaching per capita levels similar to China and South Korea, Cuomo said.
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The U.S. has suffered from a severe lack of testing.
There are nearly 20,000 confirmed cases nationwide, and 275 reported deaths, according to Johns Hopkins University.
There is a 15 per cent rate of hospitalization rate for the virus across the state, Cuomo added.
Cuomo said he remained concerned parks in the city were seeing larger gatherings, in defiance of social distancing rules, and remained worried this would lead to wider spreads.
He also called on citizens to stop hoarding and reminded them to be kind to grocers, health care workers and public servants still on the job.
“Society functions, everything works. There is going to be food in the grocery stores,” Cuomo said, wondering: “Where do you even put 100 rolls of toilet paper?”
He noted people are struggling with emotional issues, because of isolation, on top of economic hardships, as workplaces are closed.
New York would ramp up social services including counselling.