Donald Trump is still leading the Republican race for the White House after causing further controversies in the first debate in Cleveland.
His refusal to rule out a third-party run drew boos from the audience on Thursday night.
Donald Trump stood by offensive comments he has made in the past about women.
The ten candidates in Cleveland, selected by Fox News on the basis of recent national polls, provided a frank and bruising exchange of views.
Facing some tough questions from the debate moderators, the candidates tried to stand out in a crowded Republican field.
Donald Trump stumbled on his past support for a national healthcare system but his most uncomfortable moment came when moderator Megyn Kelly challenged him on his views about women.
“You’ve called women you don’t like fat pigs, dogs, slobs and disgusting animals,” Megyn Kelly said.
The tycoon answered by joking that he only said that about actress Rosie O’Donnell and stating that political correctness was one of the country’s biggest problems.
The crowd became hostile when Donald Trump said he would run as an independent, an admission that enraged Rand Paul.
“He buys and sells politicians of all stripes,” said the senator.
One of the loudest rounds of applause was for Marco Rubio when he mocked Hillary Clinton, who leads the Democratic field.
“First let me say, I think God has blessed us. He’s blessed the Republican Party with some very good candidates. The Democrats can’t even find one.”
On August 6, the Democratic Party announced it would hold its first debate in Nevada in October, hosted by CNN.
By next summer, each party will have a presidential nominee who will do battle in the race for the White House. Votes will finally be cast in November 2016.
The Republican field is one of the largest in recent years. Seven other candidates took part in an earlier debate that featured several attacks on Donald Trump.
Former Texas Governor Rick Perry said Donald Trump was running a campaign based on celebrity, while former Hewlett-Packard CEO Carly Fiorina mocked him over his Clinton ties.
While the debates were going on, Hillary Clinton was in Los Angeles for a campaign fundraising event attended by several celebrities, including reality TV star Kim Kardashian and her husband, Kanye West.