Republican frontrunner Donald Trump has attacked Ted Cruz over his birth in Canada, saying it raised 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.
Mr Cruz defended a controversy over his campaign finances in 2012, alleging bias in the media
And he said Mr Trump embodied “New York values,” saying “not a lot of conservatives come out of Manhattan – I’m just saying”
Mr Trump defended his call for a halt on Syrian refugees, saying they were a “Trojan horse” bringing in people who would harm the US
But he came under fire from Florida Governor Jeb Bush for proposing a ban on Muslims coming to the US
Florida Senator Marco Rubio said Mr Obama would confiscate every gun in the US if he could
The candidates bickered over how to respond to China’s impact on the US economy.