But Cruz fired back, saying the real estate mogul "apparently lost it," shouting "liar, liar" like a grade school student and claimed that "internal poll numbers in South Carolina must be plummeting following that debate."
Cruz has said Trump is pro-abortion, against the Second Amendment and would appoint a liberal judge to replace the recently deceased Scalia, which Trump argues is not the case.
"For instance, he talks about me being against the Second Amendment," Trump said during a press conference in Hanahan, SC. "I am the strongest person running in favor of the Second Amendment. I'm a member of the NRA, my sons have been long-term members of the NRA and they're extraordinary shots."
Trump went on to say that he plans to bring a lawsuit against the Texas senator if he doesn't apologize.
“He'll apologize but I don't want an apology after the election, I want the apology before," Trump said. "If he doesn't, I'm going to bring a lawsuit because in my opinion based on what I've learned over the last two or three days from very top lawyers, he doesn't even have the right to serve as president or even run as president. He was born in Canada. So I will bring that lawsuit if he doesn't apologize.”
Trump has raised the issue of Cruz's citizenship as a possible barrier to a presidential run, but Cruz has maintained he is a "natural-born citizen" as is constitutionally prescribed.
Trump reasoned that his lawsuit is a "favor" to the Cruz campaign because he believes Democrats inevitably will file a similar suit. He has also asked Cruz to go before a judge to have the matter settled immediately.
"If Cruz ever got the nomination, the Democrats are going to file the lawsuit," Trump said. "So in a sense I'm doing him a favor because I'm filing it early."
But Trump maintained nonetheless that Cruz was too unstable to be president.
"Yes, I would say that's true," Trump said Monday.
"He is the single biggest liar I’ve ever come across, in politics or otherwise, and I have seen some of the best of them," Trump said in a statement. "His statements are totally untrue and completely outrageous. It is hard to believe a person who proclaims to be a Christian could be so dishonest and lie so much."
Cruz blasted Trump in an event Monday -- saying that the business mogul "apparently lost it" at his press conference.
“I think the people of South Carolina deserve a campaign focused on issues, and substance, and record. But I will continue pointing out the truth about records,” said Cruz to an enthusiastic crowd in Camden, South Carolina.
“It is not a response simply to start yelling louder and louder ‘liar, liar, liar’ whenever anyone points to the candidate’s own record. Truth matters. And we are not in grade school where you just get to say ‘liar, liar, pants on fire’ and not respond to the substance.”
The senator offered a dig at Trump saying the only explanation for Trump's presser must be that his "internal poll numbers in South Carolina must be plummeting following that debate."
"The stakes are too serious for continuing like it's a circus," he also said.
ABC's Jessica Hopper contributed to this report.