As he made the announcement, the president cited the case of Hayden Williams, a young activist who was beaten up last month as he was recruiting for a conservative organization at the University of California at Berkeley — long one of the leading centers of liberal academic thought.

“If they want our dollars, and we give it to them by the billions, they’ve got to allow people like Hayden and many great young people, and old people, to speak,” Mr. Trump said, drawing huge applause.

Mr. Trump invited Mr. Williams, who was in the audience, to address the crowd briefly, calling him strong and urging him to sue the university because of the episode. Mr. Williams thanked the president for supporting young conservatives such as himself.