(AP) -- Republican front-runner Donald Trump rehashed unsubstantiated claims Tuesday that his rival Ted Cruz's father has links to President John F. Kennedy's assassin, Lee Harvey Oswald.

In a telephone interview broadcast by Fox News on Tuesday, Trump cited a National Enquirer story that claimed Rafael Cruz appeared in a 1963 photo in New Orleans with Oswald and others as Oswald distributed pro-Cuba leaflets. The Cruz campaign immediately denounced the claims as "garbage" and Trump offered no proof beyond citing the supermarket tabloid.

"His father was with Lee Harvey Oswald prior to Oswald's being, you know, shot," Trump said. "Nobody even brings it up, I mean they don't even talk about that. That was reported and nobody talks about it."

Trump's mention of the story about Rafael Cruz, a minister and Cuban immigrant who has been an active surrogate for his son's campaign, came as voters in Indiana were voting in the state's crucial presidential primary. Trump has said the Republican Party's nominating contest "would be over" if he wins Indiana.

"It's sad that the media is enabling this nonsense," Cruz's spokeswoman Alice Stewart said Tuesday. "It's a garbage claim -- let Donald talk about garbage, Ted will talk about jobs, freedom and security for the American people."

Trump has a history of repeating unproven and unsubstantiated stories, many from the National Enquirer, which has endorsed his candidacy. After the tabloid printed a story without evidence that claimed Cruz was having an extramarital affair, Trump praised the publication for having a "very good" record of accuracy.

On the campaign trial, the celebrity businessman frequently trots out a discredited tale about Gen. John Pershing, whom Trump has repeatedly claimed helped to quell Muslim extremists in the Philippines by shooting them with bullets dipped in pigs' blood.

Trump has also appeared on conspiracy theorist Alex Jones' radio show and has repeatedly peddled rumors about Muslims celebrating in New Jersey after the Sept. 11 terrorist attacks. Trump also spent years raising questions about President Barack Obama's country of birth and has allowed false suggestions that Obama is a Muslim, not a Christian, to be raised at his campaign events without correction.

In the Tuesday morning interview, Trump also railed against the elder Cruz for comments he made imploring "every member of the body of Christ to vote according to the word of God" by voting for his son. Trump questioned why Cruz should be allowed to frame the campaign in religious terms.

"I think it's a disgrace that he's allowed to say it," said Trump. "It's disgraceful that his father can go out and do that."

That's a shift in rhetoric for Trump, who while campaigning in Iowa and across the South often talked about how pastors should feel free to engage in political speech and vowed to eliminate restrictions that put churches' tax-exempt status at risk. Indiana has the largest percentage of evangelical voters of any state yet to hold its primary contest.

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Colvin reported from Detroit. Associated Press writer Scott Bauer contributed reporting from Indianapolis.

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