This article has been updated.
HANAHAN, South Carolina — The feud between Donald Trump and Ted Cruz may be headed to court.
Moments after Trump took the podium at a press conference here, his campaign released a statement threatening to take Cruz to court to challenge his eligibility to be president "if he doesn't take down his false ads and retract his lies."
"One of the ways I can fight back is to bring a lawsuit against him relative to the fact that he was born in Canada and therefore cannot be president," the statement said.
When asked by reporters about the timeline on the lawsuit, specifically if the suit would be filed before Saturday's South Carolina primary, Trump said "maybe, if I can," noting that he has to be get the papers drawn. But, he assured, it would be a quick process.
Trump has pushed Cruz's birth to an American mother in Calgary, Canada, into the spotlight of a heated GOP presidential primary. Because Cruz was born to an American citizen, U.S. immigration law says he earned citizenship as well. But the Constitutional mandate that the president must be a "natural born citizen" has not definitively been settled by the courts.
Cruz, who was also campaigning in South Carolina on Monday, told a crowd he has "no intention of responding" to Trump's latest comments and said the real-estate mogul must be "rattled."
This latest threat comes amid a litany of attacks unleashed early Monday afternoon during a local Republican hosted luncheon in Mount Pleasant.
Trump spent the bulk of his remarks hitting the Texas senator for being a "liar," citing his campaign's attempts to deceive Ben Carson supporters into thinking Carson was ending his campaign ahead of the Iowa caucuses and a controversial mailer that went out in the Hawkeye State suggesting residents could face a penalty for not caucusing.
Trump said Cruz is "the most dishonest politician" he's ever met and called his rival "unstable."
He also called Cruz "very, very weak" on immigration and questioned the senator's commitment to his stance on same-sex marriage, telling the room that Cruz will "look at his donors" to find where his allegiances actually stand.
But Cruz was not the only target during Trump's press conference - which he says was originally convened to discuss Guantanamo Bay. Trump said that he would not only keep Guantanamo open, but also increase the detainee population there "as we capture other people who are terrorists and the like."
"They should not be closing it in any way, shape, or form," Trump said of Gitmo. "I'd keep it open."
Then, pivoting to a local issue, he added that he doesn't "want people coming into this area." This, a reaction to reports from September of last year that the Pentagon is considering the Charleston-area as a place to relocate some of these detainees.
This article first appeared on NBCNews.com.