Republican presidential hopefuls Ben Carson and Donald Trump participate in the Republican Presidential Debate at the Ronald Reagan Presidential Library in Simi Valley, California.

Reuters/Simi Valley, California

Republican front-runner Donald Trump traded jabs with former Florida Governor Jeb Bush, former business executive Carly Fiorina and other presidential rivals in a contentious debate on Wednesday marked by frequent bickering and personal attacks.

In the second debate of the 2016 Republican White House race, the candidates battled over Iraq, condemned President Barack Obama's nuclear deal with Iran and sharply disagreed on whether the government should be shut down in order to cut funds for the women's health group Planned Parenthood.

With Trump shooting to a big lead in opinion polls in the Republican presidential race, the other 10 candidates on the crowded debate stage struggled at times for attention barely four months before the first nominating contest for the November 2016 election.

But unlike last month's first debate, when most of the contenders shied away from directly challenging Trump, several candidates engaged in sometimes fierce personal exchanges with the real estate mogul and former reality-TV star.

Revelling in the spotlight, Trump touted his business experience and fired off insults, making a crack about US Senator Rand Paul's looks and declaring that former New York Governor George Pataki "couldn't get elected dogcatcher."

Trump drew a sharp rebuke from former Hewlett-Packard Chief Executive Fiorina for his recent comment in an interview that voters might not back her because of her face.

"I think women all over this country heard very clearly what Mr. Trump said," Fiorina said, drawing applause.

Trump leaned toward her and replied: "I think she's got a beautiful face, and I think she's a beautiful woman."

Twitter later reported that Fiorina's response to Trump on her looks was the most Tweeted moment of the debate.

Fiorina has been rising in the polls and was sharing the stage with the leading candidates for the first time. She noted Trump's companies had filed for bankruptcy four times and asked, "Why should we trust you?"

Bomb-throwing rhetoric

Bush, a frequent target of Trump's jibes for his "low-energy" campaign, criticised the billionaire for his past friendliness with Democrats and for trying to get involved in casino gambling in Florida.

"He asked Florida to have casino gambling and we said no," Bush said. Trump shrugged his shoulders dismissively and denied trying to get into the casino industry in Florida. "Wrong... Jeb, come on." He added: "More energy tonight? I like that."

Bush, an establishment Republican, has been overshadowed by Trump's bomb-throwing rhetoric in the contest to become the party's candidate for the November 2016 presidential election but had promised to be more aggressive in the debate.

When Trump noted he was the only person on the stage who had disagreed with the decision to go to war in Iraq, Bush leaped to the defence of his brother, former President George W. Bush, who ordered the invasion.

"He kept us safe," Bush said. Trump responded: "Do you feel safer now? I don't feel so safe."

Trump also took aim at Paul, saying he did not even belong on the stage because of his low standing in the polls. Paul, a senator from Kentucky, criticised Trump for his "sophomoric" criticisms of people's appearance.

"I never attacked him on his looks, and believe me there's plenty of material there," Trump said.

Reuters/Ipsos opinion polling shows Trump leading the 2016 race among Republicans with 32%. Retired neurosurgeon Ben Carson is second at 15%. Bush is in third place at 9% as his campaign struggles to take off.

Also debating in the main event at the Ronald Reagan Presidential Library in Simi Valley were Scott Walker, Ted Cruz, Marco Rubio, Mike Huckabee, John Kasich and Chris Christie.