Media playback is unsupported on your device Media caption A history of calling Barack Obama a Muslim

Donald Trump has been criticised for failing to correct a supporter who said US President Barack Obama was a Muslim and "not even an American".

The Republican sought to laugh off the comment, which was preceded by the supporter saying: "We have a problem in this country - it's called Muslims".

The comments were made at a campaign rally for Mr Trump in New Hampshire.

Democratic frontrunner Hillary Clinton said his failure to denounce "hateful rhetoric" was "disturbing and wrong".

Pointing to his first questioner at the campaign event in Rochester, the billionaire businessman said: "I like this guy."

"We have a problem in this country called Muslims," the man said. "We know our current president is one. You know he's not even an American."

"We need this question?" Mr Trump said, laughing.

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

Media playback is unsupported on your device Media caption Republican Donald Trump sought to laugh off the comments

Mr Trump failed to clarify that Mr Obama is a Christian American, instead replying that "bad things are happening" and saying he would look into them.

Mrs Clinton joined criticism of Mr Trump on social media, tweeting: "Donald Trump not denouncing false statements about POTUS & hateful rhetoric about Muslims is disturbing & just plain wrong. Cut it out."

In a statement, Democratic National Committee chair Debbie Wasserman Schultz said Mr Trump's "racism knows no bounds".

Image copyright Reuters Image caption Mr Trump was greeted by a marching band before the campaign rally in New Hampshire

Mr Trump's campaign manager Corey Lewandowski sought to play down the incident, telling US media that "all he heard was a question about training camps".

"The media wants to make this issue about Obama. The bigger issue is that Obama is waging a war against Christians in this country," Mr Lewandowski told the Washington Post.

The incident evoked a moment during the 2008 campaign when Republican nominee John McCain took the microphone away from a woman who said she did not trust Mr Obama because he was "an Arab".

President Obama, who has spoken openly about his Christian faith, was born to an American mother and Kenyan father in Hawaii.

But Mr Trump has been one of the leading sceptics, challenging Mr Obama in 2011 to produce his birth certificate to disprove rumours that he was born in Kenya, which the president did.

With more than a year until polling day, the businessman is ahead of his Republican rivals in the polls despite having no political experience.

2016 hopefuls

Image copyright AP Image caption Clockwise from top left: Donald Trump, Jeb Bush, Scott Walker, Marco Rubio, Bernie Sanders, Hillary Clinton

The early Republican frontrunner is Donald Trump

Hillary Clinton will have learnt much from her failed campaign of 2008

Florida senator Marco Rubio lost some right-wing fans by backing a bipartisan immigration reform package

Wisconsin governor Scott Walker appeals to both the Republican establishment and the Tea Party

Libertarian Rand Paul has his supporters - and enemies - among Republicans

Veteran congressman Bernie Sanders is drawing huge crowds at his rallies

Meet all of the 2016 hopefuls