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On Thursday, Cuomo said during a news briefing that coronavirus infections have increased among young people compared with other age groups, which is posing a threat to the state's reopening plans.
Infection rates in every age group in New York have either remained flat or declined — except for people between 21 and 30 years old, according to the governor. That age group makes up an increasingly larger share of new cases over the last two weeks, he said while referring to a chart displayed at the press conference.
"To young people: This is not the time to fight for your right to party. I respect your right to party, I fully respect it. I would enshrine it in the state law, if you want to know. You have the right to party, but let's be smart about it," he said.
Cuomo also said earlier this week that the state liquor authority has suspended 27 bar and restaurant alcohol licenses for violations of social distancing rules.
"We are quite serious about it," he said, adding that the state has filed 410 charges against New York eating and drinking establishments.
The governor has previously threatened to close businesses that violate public health measures. Citing "significant evidence of failure to comply" at restaurants and bars in New York City, he said the state will close restaurants after three violations.
— CNBC's Noah Higgins-Dunn contributed to this report.