The state has conducted 45,437 tests, he said, and now has a total of 10,356 coronavirus cases.
"The more tests you take, the more positives you find," he said, adding that New York is now conducting more tests per capita than China or South Korea.
The governor also said that because the federal government on Friday declared New York a "major disaster" the state is eligible for Federal Emergency Management Agency (FEMA) aid. He said FEMA is now helping to get temporary hospitals up and running in the state.
New York City alone has 6,211 cases, an increase of 1,800. Case number increases are slowing in Westchester County while they are growing on Long Island.
The state's rate of hospitalization is now 15 percent of coronavirus cases, the governor said.
Cuomo said the state anticipates that between 40 and 80 percent of New Yorkers will be infected with coronavirus, however, authorities hope to spread out the rate of infection in order to not overwhelm the state's health system.
State officials are meanwhile "literally scouring the globe" for additional medical supplies, he said.