Donald Trump said Tuesday that he's still "seriously" considering a lawsuit challenging Ted Cruz's eligibility to run for president, after having said he'd only drop the suit if Cruz apologizes for running false ads against him.

"I'm thinking about it very seriously George, I already have a lawyer, we're looking at it very seriously, we're thinking about it," Trump told ABC's George Stephanopoulos Tuesday morning. "He was born in Canada [and] lived there for years ..."

Trump added that "many great lawyers" seem to agree with his argument that Cruz may not be qualified to run because he was born in Canada. On Monday, he said the suit could be filed "quickly."

Shortly after suggesting that Cruz seek a "declaratory judgment" from a federal judge about whether he's qualified to be commander-in-chief, Trump began using Cruz's birth status as a line of attack in his stump speech and in the GOP debates. At the fifth Republican primary debate in January, Trump told the Texas senator, "there's a big question mark over your head" related to whether he could serve as president. The real estate tycoon has also argued that Cruz would face significant legal challenges from Democrats over his presidential eligibility should he make it to the general election as the GOP nominee.

Cruz has repeatedly pushed back against the legitimacy of legal challenges over his birth status. On Monday, the first-term senator claimed his leading opponent is lashing out at him because he feels threatened by Cruz's recent attacks against his conservative credentials.

"I pointed out Donald's record of being pro-choice for 60 years, of supporting partial-birth abortion. And I pointed out that Donald, even today, supports taxpayer funding for Planned Parenthood," Cruz told Fox News' Sean Hannity on Monday night. "And Donald ... began screaming 'liar, liar.'"

"It's a very odd strategy of trying to hide your record from the voters and just screaming insults and screaming 'liar,' but the good thing is, the people of South Carolina will get to the bottom of the truth and they'll look at records," he added.

Trump, however, said he's continued to go after Cruz because he doesn't think his opponent is honest.

"Let me just say, I've dealt with many people over my lifetime, and I've been very successful, and I've dealt with some people a lot tougher than him, but I've never dealt with anybody that lies like him," Trump said.

He added, "Ted Cruz is a liar, I mean he really just outright lies. He'll say whatever he wants to say."

"I actually think he's a very unstable person, I really believe that. I think he's a very unstable person," Trump charged. "But I've never had somebody take something that you believe in and just say the exact opposite."