VATICAN CITY—Pope Francis responded for the first time to an accusation that has dogged his pontificate since last year, denying that he knew about former Cardinal Theodore McCarrick’s history of sexual misconduct before it was revealed by a church investigation.

“I knew nothing about McCarrick, obviously, nothing, nothing,” the pope said in an interview with Mexico’s Televisa network, according to a transcript published Tuesday by an official Vatican news outlet, Vatican News. “I knew nothing about McCarrick, otherwise I...