Cuomo said 779 people had died in the last 24 hours, bringing the total death toll in New York state from COVID-19 to 6,268.
The previous high of 731 was set on Monday.
New York is bearing the brunt of America's deadly coronavirus pandemic, accounting for around half the number of deaths across the country.
The governor said that despite the rise, the hospitalization rate was continuing to decrease because of social confinement orders.
"We are flattening the curve," the governor told reporters.
He added that if the rate continues to go down the hospital system will stabilize over the next two weeks, which will "minimize" the need for temporary hospitals.
Field hospitals have been set up in Central Park, at the home of the US tennis center, in a convention center and on a US navy ship to deal with the influx of patients.
Cuomo said the death toll was high because people put on ventilators when hospitalization rates soared in previous weeks were now passing away.
On Monday, the governor extended the state-wide shutdown of schools and non-essential businesses until April 29.
He again implored residents to continue to stay at home unless absolutely necessary.
"It's not a time to get complacent. It's not a time to do anything different than where we've been doing," Cuomo said.
"We are in the midst of it. We're not through it. It's not over," he added.COVID-19 has killed almost 13,000 people in the United States, and the number of confirmed cases has grown to more than 401,000, according to a running tally by Johns Hopkins University.
New York City Mayor Bill de Blasio said this week that New York's death toll could be higher because many deaths occurring at home are not being counted.Meanwhile, preliminary data released Wednesday showed that New York's Latino and African-American communities were dying of COVID-19 at a higher rate than whites.
In multi-ethnic New York City, Hispanic people made up 34 percent of deaths while comprising 29 percent of the population.
Black people represent 28 percent of fatalities while comprising 22 percent of the population.
Whites make up 27 percent of the death toll and are 32 percent of the Big Apple's population.
"It always seems that the poorest people pay the highest price. Why is that?" Cuomo asked. (AFP) RAXRAX