This comes after what the governor said was the highest one-day death toll in the state since the outbreak began, with 779 people dying on Tuesday.
"I am directing flags be flown at half-mast in honor of those we have lost to this vicious virus," Cuomo tweeted Wednesday. "They are in our hearts."
Cuomo noted during a Wednesday press briefing that so far 6,268 New Yorkers have died from COVID-19, compared with 2,753 who died in the World Trade Center attack on Sept. 11, 2001.
"Every number is a face," he said.
Cuomo said that social distancing practices appear to be helping, as the curve of cases has been flattening. He noted that this week's deaths are a result of cases that developed in the past weeks, but said the lower number of new cases is encouraging.
Still, Cuomo warned not to ease up on social distancing.
"That curve is flattening because we are flattening the curve by what we are doing. If we stop what we are doing, you will see that curve change," he said.