During a phone interview on "Fox and Friends," Trump mentioned a tabloid story claiming Rafael Cruz was with Oswald before the assassination.

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"His father was with Lee Harvey Oswald prior to Oswald being shot. I mean, the whole thing is ridiculous," Trump said. "Nobody even brings it up; they don't even talk about that.

"What was he doing with Lee Harvey Oswald shortly before the death, before the shooting?" Trump asked.

The National Enquirer published images last month of what it said showed Rafael Cruz and Oswald passing out leaflets in 1963 in New Orleans, a few months before the JFK assassination in Dallas.

"It is garbage," Cruz communications director Alice Stewart told The Hill in an email Tuesday. The campaign also called Trump " detached from reality ."

Trump spokeswoman Katrina Pierson on Tuesday defended Trump bringing up the claim, noting the story got mainstream coverage from the Miami Herald. "Really, it was just a shock and awe that it showed up in the Miami Herald," Pierson said during an interview with MSNBC's Steve Kornacki. The newspaper noted the claim has not been corroborated and that Cruz's campaign denied it. "Is there some suggestion, though, that his father had something to do with the Kennedy assassination?" Kornacki asked. "Oh, I don't know, and I think that's why it was shocking and I think why Mr. Trump mentioned it, when the Miami Herald reported it, so I guess they're looking into that," she added. Cruz's campaign dismissed the tabloid story as "garbage" last month, with Stewart telling McClatchy, "The story is false; that is not Rafael in the picture."

Trump was pushing back on Rafael Cruz's call for Christians to support his son in the Indiana primary on Tuesday, which Trump called " disgraceful ."

— Updated at 9:50 a.m.