Trump angers friends and foes

Donald Trump's support for registering US Muslims in a database drew criticism Friday from rival Republicans and Democratic presidential frontrunner Hillary Clinton, amid bursts of controversial rhetoric from GOP candidates.

Trump, leading the polls for the Republican nomination, has made several belligerent remarks about Muslims and Syrian refugees in the wake of last week's attacks in Paris claimed by the Islamic State extremist group.

Trump was asked by NBC News on Thursday whether he would support creating a database system to track Muslims.

"I would certainly implement that. Absolutely," Trump told the network at a campaign stop in Iowa.

Trump was later asked whether there was a difference between requiring Muslims to register today and Jews registering with Germany's Nazis in the 1930s.

"You tell me," Trump responded.

Clinton slammed Trump's remarks as "shocking rhetoric."

"It should be denounced by all seeking to lead this country," she wrote on Twitter.

Republican candidate Jeb Bush, who has suggested Christian refugees should be prioritised over Muslims, laid into Trump, saying Americans do not have to abandon their values to fight extremism.

"You talk about internment, you talk about closing mosques, you talk about registering people, and that's just wrong," Bush told CNBC Friday.

"That's not strength, that's weakness."

By mid-day Friday, Trump appeared to walk back his remarks, although he stood firm on the need for vigilance in tracking extremists.

"I didn't suggest a database -- a reporter did," Trump tweeted to his five million followers.

Ben Carson, a top Republican presidential contender, pushed back against Trump.

"If we're just going to pick out a particular group of people based on their religion, based on their race... that's setting a dangerous precedent," he told reporters in New Hampshire.

Carson made his own controversial comments after the Paris attacks, including Thursday when he equated the threat of extremists slipping into the country as refugees with the threat of a "rabid dog."

Senator Ted Cruz, who has been reticent to directly attack Trump on the campaign trail, is opposed to Syrian Muslim refugees reaching US shores.

But Cruz said he opposed a Muslim database on the grounds it would infringe on American religious liberty.