New York Governor Andrew Cuomo said colleges with more than 100 Covid-19 cases may have to switch to remote learning.
The state health department is issuing regulations to require colleges to notify the state when they have 100 cases in two weeks.
Seven, including Cornell and Hofstra, have seen outbreaks, Mr Cuomo said at a virus press briefing. He stated that if primary and secondary schools see a cluster, the state also will step in.
This weekend there was a large gathering of New York University students in Washington Square Park in Manhattan, Mr Cuomo said, adding that city enforcement officials and NYU security failed to break it up. It went on for hours, and several people weren't wearing masks, he said.
"What do you think is going to happen?" Mr Cuomo said.
More than 100 colleges around the country have reported more than 100 cases each, according to Mr Cuomo.
Hofstra, which is on Long Island, afterwards said Mr Cuomo's statement was "misleading" and that it had only 34 cases since Aug 28.
"In every instance, appropriate protocols have been followed, with immediate isolation and quarantine in coordination with the Department of Health," according to the school.
In related developments: New York and neighbouring New Jersey added four statesMaryland, Ohio, West Virginia and Delawareto the 14-day quarantine list and removed Puerto Rico and the US Virgin Islands, bringing the total to 35 states and territories.
Mr Cuomo said if local governments can provide enforcement, then the state will consider reopening restaurants for indoor dining in New York City.
"It would be negligent and reckless to open indoor dining, knowing that you have issues in upstate New York, knowing that compliance is going to be a problem, and knowing that you have no enforcement mechanism," he said.