Trump told DailyMail.com that, should he become president, he's not sure he'll want the former Texas solicitor general on the court.
"That's a big decision. But there's a whole question of uniting, and there's a whole question as to temperament," he said on Monday. "And I'd have to think about it."
The billionaire businessman told The Washington Post this week that he'll announce a list of 10 to 12 judges from which he'll pick replacements for the current Supreme Court vacancies.
"I'm going to announce that these are the judges, in no particular order, that I'm going to put up," he explained. "And I'm going to guarantee it. I'm going to tell people. Because people are worried that, 'Oh, maybe he'll put the wrong judge in.' "
Sally Field Calls Donald Trump Overrated
And it's Cruz's "tough temperament" that will maybe get him eliminated, Trump said. "You have to be a very, very smart, rational person in my opinion, to be a justice of any kind at a high level or low," Trump told the Mail. "You need a proper temperament. And that would be a question that I would have."
Later, ahead of Tuesday's Indiana primaries, Trump launched another attack at his opponent, accusing Cruz's father, Rafael Cruz, of being with Lee Harvey Oswald right before President John F. Kennedy's murder in 1963. The story – fueled by a photo that allegedly showed Rafael with Oswald – was originally published by the National Enquirer, and has been slammed by Cruz's campaign as false, according to the Miami Herald.
"What is this, right prior to his being shot, and nobody even brings it up," Trump said to Fox News. "They don't even talk about that. That was reported, and nobody talks about it... I mean, what was he doing – what was he doing with Lee Harvey Oswald shortly before the death? Before the shooting?"
As if the Kennedy assassination wasn't enough to pile on, Cruz has also been the subject of Internet memes questioning if he's really the Zodiac killer – wild talk that was popularized when Comedy Central host Larry Wilmore said it, repeatedly, in his remarks at the White House Correspondents' Dinner on Saturday night. Cruz's wife, Heidi, called it "a lot of garbage out there," when asked on Monday about the memes and Wilmore.
"Well, I've been married to [Cruz] him for 15 years, and I know pretty well who he is, so it doesn't bother me at all. There's a lot of garbage out there," Heidi told Yahoo News on Monday as she campaigned in Carmel, Indiana.
Cruz needs to win the Indiana primary on Tuesday to maintain his chances of keeping Trump from securing the GOP nomination with the majority of delegates.
On Tuesday afternoon, the Texas senator blasted his opponent to reporters in Evansville, Indiana, calling the GOP frontrunner a "serial philanderer," "pathological liar" and a "narcissist."
"This man is a pathological liar," he said in response to Trump's attack on his father. "He doesn't know the difference between truth and lies. He lies practically every word that comes out of his mouth."
"Donald Trump is a serial philanderer and he boasts about it," Cruz added. "This is not a secret, he is proud of being a serial philanderer ... Describes his battles with venereal diseases as his own personal Vietnam."
Trump responded by releasing a statement calling Cruz "a desperate candidate trying to save his failing campaign."
"It is no surprise he has resorted to his usual tactics of over-the-top rhetoric that nobody believes," the statement read. "Over the last week, I have watched Lyin' Ted become more and more unhinged as he is unable to react under the pressure and stress of losing, in all cases by landslides, the last six primary elections – in fact, coming in last place in all but one of them."
"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."