WASHINGTON: Donald Trump, his face red with emotion, lashed out at rivals Jeb Bush and Ted Cruz on Saturday at the most acrimonious debate to date between Republican presidential candidates, shouting insults and casting aside a pledge to be more measured.

The New York billionaire went into the CBS debate with a head of steam, having won New Hampshire last Tuesday and holding a big lead in polls in South Carolina a week before Republicans vote on Feb 20.

Rather than play it safe, Trump responded to every comment leveled his way, interrupted his opponents at will and called them liars repeatedly in an emotional outburst that could raise more questions about whether he has the temperament to serve in the White House.

He made his most blistering attacks against Bush and his brother, former President George W. Bush, who has many admirers in the Republican establishment.

It was hard to declare a winner in the debate amid the constant volley of insults, not all of them from Trump.

Cruz and fellow Senator Marco Rubio also took pointed jabs at each other over illegal immigration.

But Trump dominated the debate conservation on Twitter with 40 per cent of the mentions, according to data from the micro-blogging platform.

Trump's combative style has set the tone for much of the campaign but in recent days he had pledged to pursue a more measured, positive approach.

At the debate, that strategy lasted only through his comments about Supreme Court Justice Antonin Scalia, who was found dead on Saturday.

Trump was quickly goaded when Bush criticised Trump's past statements that Russia has a role to play in Syria. Russia, Bush said, is not attacking members of the militant Islamic State (IS) group but instead helping Syrian President Bashir Assad, who Washington wants to leave power.

Trump blasted Bush's brother for launching the Iraq war in 2003 over claims, later proven false, that Iraq possessed weapons of mass destruction.

"A big, fat mistake," said Trump, noting that the Sept 11, 2001, attacks had also occurred on Bush's watch.

"George Bush made a mistake," Trump thundered. "We all make mistakes. But that one was a beauty ... They lied! They said there were weapons of mass destruction. And there were none."

Many in the crowd booed Trump and the Republican front-runner dismissed them as "lobbyists and special interests" supporting the former Florida governor.

Bush, who has wilted in the past under assault from Trump, stood firm this time. He will campaign with his brother George on Monday in North Charleston, South Carolina.

"I'm sick and tired of him going after my family,” Bush said. “My dad is the greatest man alive in my mind. While Donald Trump was building a reality TV show, my brother was building a security apparatus to keep us safe. And I'm proud of what he did. He had the gall to go after my mother," Bush said, reminding the audience that Trump had criticised his 90-year-old mother, Barbara Bush, wife of former President George H.W. Bush. "My mother is the strongest woman I know."

"She should be running," Trump responded.

Bush provoked another outburst from Trump by saying the Republican nominee should be someone "who doesn't brag, for example, that he has been bankrupt four times."

"That's another lie," Trump said. "I never went bankrupt."

Trump vs Cruz

Trump also was drawn into a fight with Cruz over whether the real estate developer is sufficiently conservative. Trump called himself a "common-sense conservative", which Cruz dismissed.

"If Donald Trump is president he will appoint liberals to the Supreme Court," Cruz said.

"You are the biggest liar," Trump said sharply.

As they tried to talk over each other, Cruz chided Trump by saying, "Donald, adults do not interrupt each other."

Ohio Governor John Kasich, who finished second in the New Hampshire primary last Tuesday and who pushes an optimistic message, called for calm.

"These attacks, some of them are personal. I think we're fixing to lose the election to [Democratic front-runner] Hillary Clinton," he said.

Cruz and Rubio renewed their battle over who is the toughest on illegal immigration with Cruz insisting that the Florida senator, as part of a Gang of Eight senators who sought a compromise on legislation in 2013, was for "amnesty" but now is against it for political purposes.

He insisted that Rubio had said in Spanish on Univision that he would not rescind an executive order signed by President Barack Obama in support of the children of illegal immigrants.

Rubio shot back: "I don't know how he knows what I said on Univision because he doesn't speak Spanish."

As the crowd roared, Rubio said Cruz is "telling lies... He's lying about all sorts of things and now he makes things up."

Before the clashes broke out, the Republican candidates urged Obama not to nominate a successor to Scalia, saying it should be up to the next president to decide.