Trump erupted over what he calls unfair attacks by Texas Sen. Ted Cruz, CBS2's Dick Brennan reported.
"I think he's a very unstable guy," Trump said Monday.
"I have never, ever met a person that lies more than Ted Cruz."
Trump says if he doesn't get an apology from Cruz he will head to court, filing a lawsuit over Cruz's citizenship.
"We will bring a lawsuit if he doesn't straighten his act out," Trump said.
Cruz, who was born in Canada, fired back at Trump.
"Donald Trump held a press conference, where he apparently lost it," Cruz said. "I mean, he was just going on and on about how I'm the most horrible person in the world because I keep repeating the things that he said. You know, it's an amazing thing. And have you noticed how rattled Donald gets when his numbers start going down?"
Meanwhile, former President George W. Bush was in South Carolina to stump for his brother, Jeb.
His appearance comes after withering criticism from Trump in the latest debate over the former president's handling of 9/11.
"There seems to be a lot of name-calling going on, but i want to remind you what my father said: 'Labels are for soup cans,'" the former president said.
On Monday, Trump once again ridiculed the idea that former president kept America safe after the terrorist attacks.
"We had the worst attack ever. By the way, after that we did OK," Trump said. "That's meaning the team scored 19 runs in the first inning, but after that we played well. I don't think so."
Jeb Bush said Trump is trafficking in 9/11 conspiracy theories.
"While Donald Trump was a reality show, my brother building a security apparatus to keep us safe," the former Florida governor said.
And South Carolina Sen. Lindsay Graham called Trump "the Michael Moore of the Republican Party."
"I hope it will take a toll on him because it shows how unfit to be president Donald Trump is, and I think Jeb Bush has gotten under his skin, quite frankly," Graham said.
Trump also said the Republican National Committee should intervene over the allegedly false Cruz ads, and if it doesn't, it is in violation of a pledge made to him.
The billionaire hinted he might run as an independent if he doesn't secure the GOP nomination.
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