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One of the deaths was a 5-year-old boy on Thursday.
At his daily coronavirus briefing in Manhattan, Cuomo said the news was “disturbing.”
“This is the last thing we need at this time,” he said.
New York hospitals have reported 73 cases involving children experiencing symptoms similar to Kawasaki disease and toxic shock-like syndrome possibly due to COVID-19.
Cuomo said the illness has been found mostly in toddlers and children of elementary school age.
"These children happen to have the COVID antibodies or be positive for COVID," he said. "But those were not the symptoms they showed when they came in to the hospital system."
He told reporters that the Center for Disease Control has asked New York to develop national criteria so that other hospitals in the U.S. will know what to look for if the case warrants.
The New York State Department of Health has issued an advisory about the inflammatory disease, called "Pediatric Multi-System Inflammatory Syndrome Associated with COVID-19," informing hospitals and doctors of the condition, as well as guidance for testing and reporting.
Cuomo said at the briefing that the number of new coronavirus cases in the state fell to its lowest level since the crisis first began in late March.
He said 226 New Yorkers had died from the virus on Friday, which was a slight increase from the 216 deaths on Thursday.
There have been more than 26,000 COVID-19 deaths in New York since the crisis began.
On Friday, Cuomo said New York has shown success in containing the virus.
"We have the beast on the run, there's no doubt about that," he said. "We haven't killed the beast but we are ahead of it."