Ted Cruz's campaign had a snappy response to Donald Trump's lawsuit threat

Sen. Ted Cruz's (R-Texas) presidential campaign fired back on Tuesday after Donald Trump called him "unstable" and threatened to sue him.

Cruz's communications director, Rick Tyler, used a pun to dismiss Trump's attacks.

"There is reason 'Trumped up' means phony," Tyler told Business Insider in an email. "He should look hard in the mirror."

The day before, Trump released a statement raging about Cruz's supposedly "fraudulent" campaign actions.

Trump has accused Cruz of running robocalls saying that Trump was not going to run in the upcoming South Carolina primary.

During a Monday press conference, Trump said the calls were "much more severe than anything that you had" during the Iowa caucuses. This was a reference to the Cruz campaign implying to its Iowa precinct captains that retired neurosurgeon Ben Carson was dropping out of the race.

The mogul has also alleged that Cruz cannot be president because he was born in Canada. Although most legal experts believe Cruz meets the Constitution's requirement that presidents be "natural-born" citizens because his mother was a US citizen at the time of his birth, Trump has repeatedly cast doubt on Cruz's eligibility.

Trump previously said on Friday that he had "standing" to sue if Cruz didn't "clean up his act, stop cheating, & doing negative ads." Trump said at the press conference that he already hired a lawyer.

"If Ted is going to continue to lie with such desperation, I have no choice but to fight back," Trump said.