 -- Ted Cruz isn't intimidated by Donald Trump's threats to sue him over a recent campaign ad that targets the real estate mogul.

"I have to say to Mr. Trump, you have been threatening frivolous lawsuits for your entire adult life," said Cruz in a press conference today. "Even in the annals of frivolous lawsuits, this takes the cake."

On Tuesday, a lawyer for Trump sent the Cruz campaign a cease-and-desist letter saying that Cruz’s campaign ad "Supreme Trust” is “completely disingenuous” and “replete with outright lies, false, defamatory and destructive statements and downright fabrications.”

The ad, released Sunday and airing statewide in South Carolina, opens with the weight of the Supreme Court vacancy left by Justice Antonin Scalia’s passing and the liberties at stake. Then, it plays bits of Trump’s 1999 interview with Tim Russert where Trump says he is pro-choice. The ad ends with a narrator saying, "We cannot trust Donald Trump with these serious decisions.”

Cruz, a lawyer who has tried cases before the Supreme Court, ticked through the merits of the case at the presser, attempting to debunk it and at the same time paint Trump as pro-choice. Cruz used props like a poster listing the Democrats to whom Trump has donated as a tool to illustrate the point he often makes: that for decades Trump supported Democratic politicians. Cruz also pondered the lawsuit’s future and the possibility of Trump being deposed under oath.

"I look forward to any lawsuit and let me note by the way, one of the things I look forward to most of all is deposing Donald Trump. And for that particular endeavor I may not use outside counsel. I may take the deposition myself. And I will say this: Whether in a deposition or in a court of law, getting Donald Trump under oath, under penalty of perjury, answering these questions? Well I’ll point out it didn't work very well for Bill Clinton. Donald Trump does not want to be under oath answering questions about his own record because his position quite simply is that anyone who points to his record is somehow lying,” Cruz said.

Trump responded with a statement saying that Cruz is "a liar and these ads and statements made by Cruz are clearly desperate moves by a guy who is tanking in the polls.”

The statement reiterated that Trump is pro-life, an advocate of the Second Amendment and that he would nominate a conservative Supreme Court justice to fill a vacancy on the court. He also threatened again to sue the Canadian-born Cruz over his eligibility to be president.

“If I want to bring the lawsuit regarding Senator Cruz being a natural-born Canadian I will do so. Time will tell, Teddy,” the statement read.

The tension between the men has escalated the last few days as the battle for the state of South Carolina intensifies. While the latest polls show Trump leading Cruz in South Carolina, a new NBC/WSJ poll shows Cruz leading Trump nationally for the first time.

During his press conference, Cruz also took aim at Senator Marco Rubio, who is nearly neck and neck with Cruz in South Carolina, according to a Bloomberg Political poll released today.

"Marco Rubio is behaving like Donald Trump with a smile,” Cruz said.

“Both Marco and Donald, their strategy is simply to yell liar, liar, liar,” Cruz added.

He also criticized Rubio for using robocalls from South Carolina Congressman Trey Gowdy, a surrogate of Rubio’s, to attack Cruz.

“Look, it's unfortunate. His campaign has not gotten the traction he wanted. I recognize that the Rubio campaign is disappointed with a third-place finish in Iowa. Disappointed with a fifth-place finish in New Hampshire. And the consultants are who running his campaign apparently made the decision that their one hope of doing well is to make false attacks with no basis whatsoever,” Cruz said.

The Rubio campaign has accused Cruz of running push polls in South Carolina attacking the Florida senator. Cruz denied having any involvement in doing so.