In the interview, Mr. Trump was asked to respond to the elder Mr. Cruz’s invocations of God as he urged evangelical voters to support his son, suggesting the alternative could mean the “destruction of America.”

“I think it’s a disgrace that he’s allowed to do it. I think it’s a disgrace that he’s allowed to say it,” Mr. Trump said, before adding, “And, you know, his father was with Lee Harvey Oswald prior to Oswald’s being — you know, shot. I mean, the whole thing is ridiculous. What is this, right, prior to his being shot, and nobody brings it up. They don’t even talk about that. That was reported and nobody talks about it. But I think it’s horrible.”

He went on, “What was he doing with Lee Harvey Oswald shortly before the death, before the shooting? It’s horrible.”