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Story highlights

Ted Cruz held a press conference Wednesday where he criticized Donald Trump and Marco Rubio

All three are in a heated battle for South Carolina, who holds its Republican presidential primary on Saturday

(CNN) —  

Ted Cruz said he is calling Donald Trump’s bluff – and Trump is refusing to take his threat to sue Cruz off the table.

Cruz slammed Marco Rubio and Trump during a dramatic news conference Wednesday that underscored the escalating tension among Republicans ahead of Saturday’s South Carolina primary.

But it was his broadside against Trump that sounded like a challenge: Sue me.

“I have to say to Mr. Trump, you have been threatening frivolous lawsuits for your entire adult life,” Cruz said at a news conference in South Carolina. “If you want to file a lawsuit challenging this ad, claiming defamation, file the lawsuit.”

Trump responded by goading Cruz, saying that “time will tell, Teddy,” as he repeated his threat of lawsuits – over a Cruz campaign ad or over his eligibility for the presidency, given the Texas senator’s Canadian birth – off the table.

The dust-up is over an ad Cruz’s campaign is airing in South Carolina that paints Trump as supportive of abortion rights – featuring a 1999 clip in which Trump calls himself “very pro-choice.”

Trump has since evolved on the issue and now says he opposes abortion rights.

Cruz said Wednesday said that Trump’s lawyers have sent his campaign a cease and desist letter ordering Cruz’s campaign to take down the spot, and the Texas senator is calling the billionaire businessman’s bluff.

“But if Donald Trump files the lawsuit that he threatens, that lawsuit will be frivolous,” Cruz said.

In a statement issued by his campaign minutes after Cruz’s comments Wednesday, Trump pointed to the Cruz campaign’s tactics in Iowa, where staffers inaccurately portrayed Ben Carson as dropping out of the race while caucus-goers were still voting.

“He is a liar and these ads and statements made by Cruz are clearly desperate moves by a guy who is tanking in the polls – watching his campaign go up in flames finally explains Cruz’s logo,” Trump said, in a reference to the flame included in Cruz’s campaign logo.

Trump later told supporters during a campaign event in Walterboro, South Carolina, on Wednesday that Cruz “stole” the caucuses, calling his actions “a disgrace.”

In the statement, Trump added: “I am pro-life and I do not support tax payer funding for Planned Parenthood as long as they are performing abortions. … If I want to bring a lawsuit it would be legitimate. Likewise, if I want to bring the lawsuit regarding Senator Cruz being a natural born Canadian I will do so. Time will tell, Teddy.”

Cruz pointed out the ad uses video of Trump and he argued that any court in the country would reject a defamation case based on use of a candidate’s own words.

And on the Florida senator, Cruz said, “Marco Rubio is behaving like Donald Trump with a smile.”

“They are right now are in the closing period of a campaign,” Cruz said, adding his campaign is “focused on any accomplishments that Rubio has.”

Cruz, Trump and Florida Sen. Marco Rubio are in a hard fought battle for the South Carolina Republican primary this Saturday. Trump has been polling ahead, with Cruz trailing in second.

RELATED: GOP candidates at war in South Carolina

On Tuesday, Trump repeatedly called Cruz a liar while speaking to the media and campaigning on the trail.

“Let me just say, I’ve dealt with many people over my lifetime, and I’ve been very successful, and I’ve dealt with some people a lot tougher than him, but I’ve never dealt with anybody that lies like him,” Trump told ABC on Tuesday morning.

Cruz said Wednesday that he was merely using Trump’s own words.

“His own words said on national television are a matter of public record, and by definition repeating someone’s own words can not be defamation,” Cruz said.

Rubio hit Cruz for “disturbing” behavior on the campaign trail, saying that his Senate colleague has mischaracterized his record.

CNN’s Sara Murray contributed to this report.