A couple of hours after Donald Trump connected Ted Cruz's father to John F. Kennedy's assassin, Cruz made an announcement to reporters that made it fairly evident that should Trump become the nominee, he will not have Cruz's support.

"I'm going to do something I haven't done for the entire campaign, for those of you all who've traveled with me, all across the country. I'm going to tell you what I really think of Donald Trump," Cruz said. "This man is a pathological liar. He doesn't know the difference between truth and lies. He lies practically every word that comes out of his mouth." And Cruz added, "The man is utterly amoral. Morality does not exist for him."

He went on to characterize Trump's rhetoric as "a mindless yell," and he called him "a narcissist at a level I don't think this country's ever seen. Donald Trump is such a narcissist that Barack Obama looks at him and goes, 'Dude, what's your problem?'"

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Cruz then lambasted Trump for alleging that his father was involved with Lee Harvey Oswald.

"Donald Trump alleges that my dad was involved in assassinating JFK. Let's be clear: this is nuts," Cruz told reporters in Indianapolis as voters in the Hoosier state headed to the polls to cast ballots in their state primary. "This is just kooky."

"While I'm at it, I should say, 'Yes my dad killed JFK, he is secretly Elvis and Jimmy Hoffa is buried in his backyard,'" Cruz joked.

The GOP presidential candidate, who has trailed behind Trump in Indiana in recent polls, said Trump's source for the allegation was the National Enquirer, which Cruz called "tabloid trash." He noted that the paper's CEO, David Pecker, is a friend of Trump's and the tabloid has endorsed him for president. Cruz said Trump uses the National Enquirer "to smear anybody and everybody" including his wife Heidi.

"Apparently she's not pretty enough for Donald Trump," Cruz said. "I may be biased, but if he's making that allegation, he's also legally blind."

It also published an article that made unsavory allegations about Cruz's private life.

Cruz called his father his hero and said he was "imprisoned and tortured in Cuba, and when he came to America, he had nothing. He had $100 in his underwear."

The tabloid ran a story last week that said it had conclusive evidence that Cruz's father is a man photographed next to Oswald in 1963, months before Kennedy's assassination.

Trump brought up the story in an interview Tuesday morning with Fox News' "Fox and Friends."

"You know, his father was with Lee Harvey Oswald prior to Oswald's being -- you know, shot," Trump said. "I mean, the whole thing is ridiculous. What is this?"

Trump added: "Right prior to his being shot and nobody even brings it up. I mean, they don't even talk about that. That was reported and nobody talks about it."

CBS News' Alan He contributed to this report.

This article has been updated to reflect that Ted Cruz characterized some of Donald Trump's comments as "kooky," not "cuckoo."