“We will bring a lawsuit if he doesn’t straighten his act out,” Trump told reporters here Monday afternoon. “This guy’s just a plain out liar.”

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Trump added, “He just comes out, and boom, boom, boom, absolute lies….He doesn’t even have the right to serve as president or even run as president.”

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For weeks now, Trump has stoked a so-called birther controversy about Cruz, questioning whether his birth in Calgary, Canada, disqualifies him from serving as president.

The Constitution mandates that only “natural born citizens” can be president, though there are varying interpretations of the law as to whether Cruz would be disqualified. Cruz has long said that because his mother was a U.S. citizen by birth, he is one as well.

At the news conference, Trump also called Cruz “a very unstable guy” and urged reporters to question the senator’s Christianity.

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“I have never seen anybody that lied as much as Ted Cruz,” Trump said. “He goes around saying he’s a Christian. I don’t know. You’re going to have to really study that.”

Cruz responded later in the day, calling Trump "rattled."

"You know, today Donald Trump held a press conference where he apparently lost it," Cruz told an audience in Camden, S.C. Cruz said that Trump called him "the most horrible person in the world" because Cruz had repeated things that Trump himself had said.

"I guess the only answer I can give for why he lost it today is this is the most rattled I’ve ever seen Donald," Cruz said.

He added, "But I guess the only explanation one could have is that his internal poll numbers for South Carolina must be plummeting.”