Republican frontrunner Donald Trump has attacked Ted Cruz over his birth in Canada, saying it raises questions about his presidential eligibility.
In the latest Republican debate for White House hopefuls, Mr Trump told his rival: “There’s a big question mark over your head.”
The constitution mandates the president be a “natural born citizen” of the US.
Issues of national security, the economy and foreign policy have also played heavily in the debate.
In the polls, the pair are leading the five other candidates, who were also on the stage in North Charleston.
The debate came just two weeks before the first real test of the campaign, when voters in Iowa pick their Republican and Democratic choices for president.
They also argued over the meaning of “New York values”, which Mr Cruz threw at the New York billionaire as a slur on his conservative credentials.
But the New Yorker said that was an insult to the “great people” who pulled together after the 9/11 attacks.
After the debate, Mr Trump told reporters: “I guess the bromance is over.”
All the candidates targeted leading Democratic candidate Hillary Clinton, who was repeatedly attacked for her time as Secretary of State.
The primary contests, in which each party picks their nominee for president, begin in February and the presidential election is in November.