Mr. Cuomo attributed much of the jump to an increase in testing. Of the 14,597 people to be tested so far, nearly 5,000 were tested on Tuesday.

In New Jersey, officials said on Wednesday that another 162 people had tested positive for the virus, raising the state’s total of confirmed cases to 427. Officials also said there had been three more deaths linked to the virus, bringing New Jersey’s total to five.

Officials in Connecticut said on Wednesday that a man in his 80s who had been hospitalized at Danbury Hospital had died from the virus, the state’s first known death linked to the virus.

In the past week, as testing has expanded and more people have gotten sick, the number of people to test positive for the virus in New York State has increased 42 percent a day on average.