Trump said in an interview with The Washington Post
that Republican voters should think twice before voting for Cruz, who could face challenges to his eligibility to serve as president given that he was born in Canada, and not the United States.
"Republicans are going to have to ask themselves the question: 'Do we want a candidate who could be tied up in court for two years?' That'd be a big problem," Trump said in the interview. "It'd be a very precarious one for Republicans because he'd be running and the courts may take a long time to make decision. You don't want to be running and have that kind of thing over your head."
Trump added that he'd "hate to see something like that get in his (Cruz's) way" and noted that "a lot of people are talking about it."
The U.S. Constitution requires the president be a "natural-born citizen."
Cruz was born in Canada, but was automatically granted American citizenship by birth because his mother was an American citizen -- which most legal scholars contend meets the "natural-born citizen" requirement. The question has never been tested in court.
Cruz responded to Trump on Twitter with a link to the iconic TV character Fonzie jumping over a shark in the TV show "Happy Days."
In a gaggle with reporters following an event, Cruz said he wasn't going to elaborate any further.
"I think I'm going to let my response stick with that tweet," he said. "Because the best way to respond to this kind of attack is to laugh it off."
Cruz held dual citizenship with the U.S. and Canada until he renounced his Canadian citizenship in May 2014.
Trump ascended to the heights of right-wing political circles in 2011 when he questioned President Barack Obama's citizenship, suggesting that Obama was not born in the United States.
Trump has gone back and forth on the issue of Cruz's citizenship, suggesting in December 2014
that Cruz's Canadian birthplace could be problematic. But last September, Trump said, "I hear it was checked out by every attorney and every which way and I understand Ted is in fine shape."
Other Republican presidential candidates are demurring from questioning Cruz's eligibility to serve as president.
Following his town hall in Dover, New Hampshire, former Florida Gov. Jeb Bush said he believes Cruz is a natural born citizen. Responding to a reporter's question Bush responded with a chuckle, "Yeah. I do. Look, yes."