As the Texas senator gains ground over the billionaire businessman, Trump used a "Fox News Sunday" appearance to refer Cruz as "a little bit of a maniac."
"When you look at the way he's dealt with the Senate, where he goes in there, like a, you know, frankly like a little bit of a maniac, you're never going to get things done that way," Trump said, a reference to Cruz's habit of bucking even his own party leader's wishes while serving in Congress.
Cruz used Twitter to respond to Trump's latest volley hours later, writing, "In honor of my friend @realDonaldTrump and good-hearted maniacs everywhere..." with a link to a YouTube video of the song "Maniac" from the movie "Flashdance."
The exchange shows how -- at least in public -- Cruz has repeatedly sought to avoid open conflict with Trump, with the hopes of not alienating any of the mogul's followers who could be wooed to support his candidacy if Trump eventually dropped out.
However, with recent polling showing the two closer than ever and one Iowa survey showing Cruz ahead, the tension between both campaigns has heightened, leading to this weekend's sparring.
It began Friday morning when reports surfaced that that at a private fundraising event Cruz questioned the judgment and electability of Trump and fellow GOP candidate Ben Carson.
Trump quickly sent a shot at Cruz, tweeting, "Looks like @tedcruz is getting ready to attack. I am leading by so much he must. I hope so, he will fall like all others. Will be easy!" and ".@tedcruz should not make statements behind closed doors to his bosses, he should bring them out into the open - more fun that way!"
Later Friday Cruz tried to dampen down the tension, responded on Twitter, "The Establishment's only hope: Trump & me in a cage match. Sorry to disappoint -- @realDonaldTrump is terrific. #DealWithIt."
By Sunday evening Trump still seemed miffed at Cruz, tweeting, "I was disappointed that Ted Cruz would speak behind my back, get caught, and then deny it. Well, welcome to the wonderful world of politics!"
On Monday morning, Cruz and his supporters continued to downplay the spat and Iowa Rep. Steve King, who endorsed the senator, explained to CNN's "New Day" that strategy.
"There's never been any wisdom in taking on Donald trump and starting a fight with him," King said.