In a TV interview, Trump made comments alleging a link between Cruz's father and Lee Harvey Oswald
Ted Cruz has reacted furiously to claims made by Donald Trump linking Cruz's father to Lee Harvey Oswald - the man who killed John F Kennedy.
In a TV interview, Mr Trump claimed Cruz's father "was with Lee Harvey Oswald prior to Oswald being shot. I mean, the whole thing is ridiculous... Nobody even brings it up".
The Guardian reports that the comments refer to a story in the American tabloid the National Enquirer, claiming Rafael Cruz was with Oswald before he shot Kennedy in Texas in 1963.
Trump's rival for the Republican presidential candidacy responded in no uncertain terms, calling Trump "a pathological liar" who does not "know the difference between truth and lies". He also called the Enquirer "tabloid trash... that just spreads blatant lies".
"This is nuts. This is not a reasonable position... this is just kooky," Mr Cruz told reporters, adding sarcastically that "yes, my dad killed JFK, he is secretly Elvis and Jimmy Hoffa is buried in his backyard".
He went on to say Trump "is utterly immoral... morality does not exist for him" and that "everything in Donald's world is about Donald".
You can see a video of Mr Cruz's comments below:
Trump went on to respond to Cruz's comments, referring to his rival as a "desperate candidate trying to save his failing campaign".
In a statement on his website, Trump said, "today’s ridiculous outburst only proves what I have been saying for a long time - that Ted Cruz does not have the temperament to be president of the United States".
The latest fiery exchanges came ahead of primaries in Indiana.
The vote is said to be one of the last chances for Cruz to save his struggling campaign and halt Trump's path to the Republican nomination. However, polls have suggested Trump could win 49% of the vote to Cruz's 34%.