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

Seneca, South Carolina (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.

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.

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