Alan Dershowitz recommended bringing the political debate "back to the center" away from the fringe groups.
"Both the hard right and the hard left engage in identity politics," the retired Harvard law professor told "Fox & Friends" on Saturday.
"I'm a centrist liberal, many of you are centrist conservatives, we can talk. We can have a rational argument."
In contrast, several recent incidents showcase the unwillingness of the extreme right and left to have a discussion, he pointed out.
Last month, violent white nationalists rioted in Charlottesville, Virginia, killing one.
At the University of California at Berkeley, conservative commentator Ben Shapiro's speech warranted ramped up security given last year's riots over conservative speakers. The violent far left group Antifa has popped up there and around the country, destroying property and injuring people, including police officers.
"I love to quote my old grandmother from Poland," Dershowitz joked. "I would come home and say 'Grandma, the Brooklyn Dodgers won.' And she would say, 'Yeah, but was it good or bad for the Jews?'"
"That was her only criteria," he said. "Why not is it good or bad for America?"
The hard right is much smaller and less influential on college campuses than hard left, Dershowitz stated, adding that Antifa "thugs" should be called a gang.
"Let's talk, not shout," he concluded.