US presidential candidate Donald Trump has drawn fire from Democrats and some Republicans after declining to rebuke a questioner at a town hall event who insulted Muslims and wrongly said President Barack Obama is a member of the faith.

The question to Trump, the front-runner in the 2016 Republican campaign, came on Thursday night at a town hall in Rochester, New Hampshire.

The first person Trump called upon said: "We have a problem in this country: It's called Muslims."

"We know our current president is one," the man said of Obama, who is Christian. "You know he's not even an American."

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Trump, a driver of the "birther" movement that falsely claimed Obama was born outside the US, first responded with feigned exasperation - "We need the question," he said, to laughs - before letting the man continue.

"We have training camps growing where they want to kill us. That's my question," the man in the audience continued. "When can we get rid of them?"

Trump replied: "We're going to be looking at a lot of different things. And you know, a lot of people are saying that, and a lot of people are saying that bad things are happening out there.

"We're going to be looking at that and plenty of other things."

Democratic front-runner Hillary Rodham Clinton condemned Trump's response after a campaign event in New Hampshire, the AP news agency reported.

"He knew, or he should have known, that what that man was asking was not only way out of bounds, it was untrue," she said.

"He should have, from the beginning, repudiated that kind of rhetoric - that level of hatefulness."

'Cynical strategy'

At the White House, press secretary Josh Earnest said on Friday that it was unfortunate that Trump "wasn't able to summon the same kind of patriotism" that Republican Senator John McCain showed in 2008, when he took the microphone away from a woman who said she did not trust Obama because he was Arab.

"Mr Trump isn't the first Republican politician to countenance these kinds of views in order to win votes," Earnest said.

"That's precisely what every Republican presidential candidate is doing when they decline to denounce Mr Trump's cynical strategy."

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But South Carolina Senator Lindsey Graham was happy to criticise Trump, saying via Twitter: "There is a right way to handle these situations and a wrong way to handle these situations, Donald."

Graham tweeted a link to a story about how he condemned a racist comment during a political event earlier this year in Iowa, and then beat the man who made it in a game of pool.

New Jersey Governor Chris Christie said that "if somebody at one of my town meetings said something like that, I would correct him."

But Christie, appearing on Friday on NBC's Today show, also said it is up to Trump to decide how to handle such situations, adding, "I'm not going to lecture him about what to do."

Others in the Republican field did not want to talk about it at all.

At a campaign event in South Carolina, Texas Senator Ted Cruz did not respond to questions about Trump or the president's faith, saying that "President Obama's faith is between him and God."

Cruz said, "We've seen the rights of Christians undermined all over the country," under Obama, adding that he "has at times acted as an apologist for radical Islamic terrorists".

'War against Christians'

Trump did not respond to shouted questions about the exchange as he left the event, but his campaign released a statement in response that focused on the treatment of Christians in the country.

"The media wants to make this issue about Obama. The bigger issue is that Obama is waging a war against Christians in this country," it read.

"Christians need support in this country. Their religious liberty is at stake."

Trump is a driver of the "birther" movement that falsely claimed Obama was born outside the US [AP]

Trump's campaign manager, Corey Lewandowski, said that the room was noisy and that Trump had trouble hearing the question.

But the questioner was speaking into a microphone, and his remarks could be heard clearly by several journalists sitting near the back of the gymnasium.

Trump was scheduled to appear on Friday night at a forum for Republican presidential candidates in South Carolina but pulled out of the event.

In a statement, his campaign said that "a significant business transaction that was expected to close Thursday" had been delayed, keeping Trump from attending.

Source: AP