WASHINGTON (Reuters) - Republican presidential hopeful Ted Cruz lashed out at rival candidate Donald Trump on the day of Indiana’s primary on Tuesday, calling him a pathological liar, narcissist and bully after the front-runner linked Cruz’s father to John F. Kennedy’s assassin.

“I’m going to tell you what I really think of Donald Trump. This man is a pathological liar. He doesn’t know the difference between truth and lies,” Cruz told reporters in a scathing indictment.

“He lies practically every word that comes out of his mouth. And...his response is to accuse everybody else of lying.”

In a television appearance earlier, Trump linked Cruz’s father, Rafael Cruz, to Kennedy assassin Lee Harvey Oswald, citing a report by National Enquirer, a supermarket tabloid known for celebrity gossip and alien sightings.

“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,” Trump said on “Fox & Friends.”

Republicans in Indiana might give New York billionaire Trump an almost unstoppable advantage in his turbulent journey toward the party’s presidential nomination.

The real estate mogul holds a double-digit polling lead in the Midwestern state over Cruz, a U.S. Senator of Texas.

Slideshow ( 3 images )

Cruz denounced the Enquirer and its chief executive, David Pecker, who has endorsed Trump, for claiming his father, a Cuban immigrant to the United States, was pictured handing out pro-Fidel Castro literature with Oswald in New Orleans in 1963.

“Yes, my dad killed JFK, he is secretly Elvis and Jimmy Hoffa is buried in his back yard,” Cruz said in a sarcastic retort.

Cruz also unleashed fury over Trump’s earlier comment about his wife, Heidi.

“Donald has a real problem with women. Donald is terrified by strong women - he lashes out at them,” Cruz said.

“The man is utterly amoral. Morality does not exist for him,” Cruz said.