U.S. Senate Minority Leader Mitch McConnell (R-Ky.) said American university presidents "need to get control" of pro-Palestinian protests on campuses across the country. But he rejected calls from fellow Republicans to bring in the National Guard to lock up all demonstrators.

"The First Amendment is important. But it doesn't give you the ability to claim there's a fire going on in a theater, because it threatens everyone else," McConnell said in prerecorded interview that aired Sunday on CBS' "Face the Nation."

"What needs to happen, at least at the beginning, is these university presidents need to get control of the situation, allow free speech and push back against antisemitism," he added.

The Kentucky Republican also said he had believed that antisemitism was "largely gone in this country."

But "we've seen a number of young people who are actually antisemitic," he said. "Why don't they all sit down and have a civil conversation rather than trying to dominate the talk? And I think the first line of defense is these university presidents."

When pressed by "Face the Nation" host Margaret Brennan, McConnell also expressed disagreement with recent remarks by House Speaker Mike Johnson (R-La.) and Republican Texas Gov. Greg Abbott.

During a visit last week to Columbia University, where more that 100 students were arrested earlier this month during a brief police crackdown on a protest encampment, Johnson told CBS News that "we need to call in the National Guard and law enforcement to take control."

Abbott has also said that "all of the protesters belong in jail."

"Let's see if these university presidents can get control of the situation. They ought to be able to do that," McConnell said. "Civil discussion is what college education is supposed to be about. I'd be interested in hearing the antisemitic people explain the justification for that kind of talk."