WASHINGTON: Donald Trump has claimed Ted Cruz's father was with Lee Harvey Oswald "shortly before" the assassination of President John F Kennedy.
Mr Trump's attack, inflammatory even by his standards, came as polls opened yesterday in Indiana, the state where he was aiming to seal the Republican presidential nomination.
Mr Cruz, his closest rival in the race, has dismissed the claims about Rafael Cruz as "garbage" and "false".
It came as the first poll emerged showing Mr Trump leading Hillary Clinton in a hypothetical general election contest between the two. The Rasmussen poll had Mr Trump on 41 per cent to Mrs Clinton's 39 per cent. An average of all polls taken so far still had Mrs Clinton with a seven-point lead.
Mr Trump turned his fire on Rafael Cruz, 77, in a national television interview. The billionaire said: "He 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 even brings it up. They don't even talk about that.
"I mean what was he doing, what was he doing with Lee Harvey Oswald shortly before the death? Before the shooting? It's horrible."
Mr Trump appeared to be basing his assertion on a report in the National Enquirer two weeks ago. That report claimed Rafael Cruz was photographed handing out pro-Castro leaflets with Oswald in New Orleans in August 1963, three months before the Kennedy assassination in Dallas, Texas.
The supermarket tabloid, which has endorsed Mr Trump, published a faded black and white photograph it claimed showed the two men together.
The photograph was impossible to independently verify and many observers were of the opinion the man in it was not Rafael Cruz.
At the time a spokesman for Mr Cruz said: "This is another garbage story in a tabloid full of garbage. The story is false. That is not Rafael in the picture."
Rafael Cruz was born in Cuba and tortured by the Batista regime before escaping to America, arriving with $100 sewn into his underpants and speaking no English.
Rafael Cruz originally supported Fidel Castro in the early 1960s but later became a passionate anti-Communist and an evangelical Christian pastor.
Mr Trump's attack came after the elder Cruz toured churches across Indiana imploring Christians to vote against the property mogul.
Around one third of Indiana's adult population identify themselves as evangelical Christians.
Rafael Cruz told them: "I exhort every member of the body of Christ to vote according to the word of God and vote for the candidate that stands on the word of God. I am convinced that man is my son, Ted Cruz. The alternative could be the destruction of America."
Mr Trump said: "It's disgraceful that his father can go out and say that. The evangelicals are angry about it, the way he does that, and I'm winning the evangelical vote."
In March Ted Cruz dismissed as "garbage and lies" another National Enquirer report that he was "hiding five mistresses". He accused Mr Trump's "henchmen" of being behind the story and trying to "slime" him.
Yesterday the Texas senator said: "Donald Trump alleges my Dad was involved in assassinating JFK. Let's be clear, this is nuts."
He added sarcastically: "I guess I should just go ahead and admit it - yes my Dad killed JFK. He is also secretly Elvis and Jimmy Hoffa [the Teamsters union boss thought to have been killed by the mafia] is buried in his back yard." Mr Cruz then announced it was finally time to say what he really thought of Mr Trump, launching into the most blistering assault on the billionaire yet made by any candidate.
Mr Cruz said: "This man is a pathological liar. He doesn't know the difference between lies and truth.
"He is a narcissist on a level I don't think this country has ever seen. The man is utterly amoral. Morality does not exist for him."
He added: "Donald Trump is a serial philanderer and he boasts about it. This is not what America is. We are not a proud, boastful, self-centred, mean spirited, bullying, hateful nation. We are staring into the abyss."
He called Mr Trump an "insecure and weak bully" who was "terrified of women".
Mr Trump later issued a statement saying Mr Cruz's diatribe showed he was "desperate and unhinged".
The billionaire said: "I have watched Lyin' Ted become more and more unhinged as he is unable to react under the pressure and stress of losing."