Hofstra University is among several colleges in New York that Gov. Andrew Cuomo mentioned by name as experiencing COVID-19 outbreaks -- but the school has pushed back against that characterization.

Cuomo said during his Tuesday news briefing that college campuses are going to "be a problem" -- citing rising cases at some universities.

"People coming from around the country and around the world to these colleges ... they go out to party and they wind up spreading the virus. Nationwide, 108 colleges have already reported more than 100 cases," says Cuomo.

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Cuomo announced a new plan to track cases and take action if necessary. He says any school that goes over 100 positive COVID-19 cases has to report them to the Department of Health. He also says if they go over 100, the school can be closed down for all-remote learning.

The tracking will be done online, with a daily report card that can be accessed by anyone. It'll be available soon on the state's Department of Health website.

"We're doing a regulation, every school district has to report every day to the Department of Health as to how many tests were taken, what type of test, what was the result," says Cuomo. "State Department of Health is going to put that on the website, we're going to have a COVID report card for every school in the state."

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Cuomo then called out several colleges by name, including Hofstra, SUNY Oneonta, Cornell University, University at Buffalo, SUNY Oswego, Colgate University and SUNY Fredonia.

While SUNY Oneonta has gone entirely online after hundreds of cases were reported, Hofstra says since Aug. 28, the school has seen 34 positive cases among a total on-campus population of 9,200.

Hofstra University officials also said in a statement, "The governor's statement is misleading ... in every instance, appropriate protocols have been followed with immediate isolation and quarantine in coordination with the Department of Health."

An official in the governor's office has since clarified that Cuomo wasn't suggesting that Hofstra had 100 cases, but did say that even 34 cases is something to keep an eye on.

In a statement, a spokesperson said, "Gov. Cuomo has been clear that COVID can easily spread on college campuses and must be monitored closely -- with 74 confirmed cases among the student body, there is obviously cause for concern at Hofstra and the Department of Health will continue to treat this like what it is: an outbreak that must be watched."