WASHINGTON - In his characteristic combative style, billionaire businessman Donald Trump dominated the first Republican presidential debate on Thursday night - jolting the event from the start by refusing to rule out running as an independent if he failed to get the party’s nomination.

A moderator of the debate, sponsored by conservative FOX News, asked all the candidates to raise their hand if they could not immediately dedicate themselves to supporting the eventual nominee of the party, and not run as a third-party candidate. Trump, standing centre stage, raised his hand. None of the other candidates did.

The moderator asked whether Trump understood that raising his hand meant he would potentially run as a third-party nominee, even though most people agreed that would likely hand the White House to the Democrats.

“I understand,” Trump said multiple times. “I can totally make that pledge if I am the nominee, I will not run as independent.” “We will win but I want to win as the Republican, I want to run as the Republican nominee,” he added.

Trump, who was greeted with a mixture of applause and boos, was also grilled over his outspoken views on immigration, women, bankruptcy and President Barack Obama’s leadership.

“I think the big problem this country has is being politically correct,” insisted the real estate billionaire and reality TV star after he was asked by debate chair Megyn Kelly of Fox News about calling women “fat pigs, dogs, slobs, and disgusting animals”.

The two-hour televised debate in Cleveland was billed as an opportunity for Trump’s rivals for the Republican primary election to put a halt to his dramatic recent rise in the polls and highlight his limits as a serious politician. But while several rivals, most notably an eloquently performing Marco Rubio, attempted more nuanced analysis over issues such as immigration, Trump’s trademark bluster was bolstered by his position in the centre of the debate stage and the fact that so many of the other candidates were talking about him.

Trump, already one of the best known and least experienced names in the 2016 race, also appeared to win the battle to win yet more public attention: appearing top in a ranking of internet search terms during the debate that was released by Google.

“Our country is in serious trouble, we don’t win any more,” trump his closing remarks. “We can’t do anything right ... We have to make our country great again.”

In contrast, Jeb Bush, the establishment favourite and former frontrunner in the polls, had a difficult night, coming under fire not just from the hosts but his fellow panelists on issues such as his support for immigration reform and nationally enforced education standards.

The night was also notable for a fierce exchange between Senator Rand Paul and Chris Christie, the governor of New Jersey, over the balance between surveillance and national security.

The two clashed in the most heated scenes of the debate over Paul’s support for curtailing the National Security Agency. When Paul accused Christie in turn of getting too close to the White House and “hugging” Obama, the New Jersey governor shot back that the hugs he remembered were with the families of 9/11 victims. Yet divisive as the NSA issue is among Republican voters, it is the most distinctive part of Paul’s agenda and his passionate defence of the bill of rights brought warm applause from the crowd.

On immigration, one of the main topics of the night, Bush defended his call for a path to legal status for some of the people living in the U.S. illegally, an unpopular position among some Republican voters who equate legal status with amnesty. “The great majority of people coming here have no other option,” Bush said.

Trump in particular has pushed the issue of immigration throughout the summer, drawing criticism for saying Mexican immigrants are rapists. He said Thursday that he had been told that by border patrol agents, and he took credit for immigration being an issue in the campaign.

“If it weren’t for me, you wouldn’t even be talking about illegal immigration,” he said, despite the fact that immigration has been a hot-button issue in presidential campaigns for years.

Seventeen Republicans are seeking the party’s nomination, but only 10 were invited by debate host Fox News to participate in the main event based on their showing in recent polls. The remaining seven were relegated to a pre-debate forum.

A raucous crowd cheered the candidates on throughout the debate in Cleveland, the same city where Republicans will nominate their general election candidate next summer. No Republican has ever won the presidency without winning Ohio.

While the candidates peppered their remarks with barbs about former Secretary of State Hillary Clinton, they avoided lengthy attacks on her record and the deadly attack in Benghazi, Libya. Only late in the debate did Wisconsin Governor Scott Walker raise the controversy surrounding her use of personal email and a private server while serving in the Obama administration.

“Probably the Russian and Chinese governments know more about Hillary Clinton’s email server than do the members of the U.S. Congress,” Walker said.