Republican presidential front-runner Donald Trump faces more criticism after he declined to correct a questioner at a town hall event who incorrectly said president Barack Obama is a Muslim.

Mr Trump, who has a history of controversial remarks about immigrants and other groups, was kicking off a town hall event in Rochester, New Hampshire - his first since Wednesday evening's second Republican primary debate.

The first man Mr Trump called on to ask a question said: "We have a problem in this country. It's called Muslims. We know our current president is one. You know he's not even an American."

Mr Trump, who was a driver of the "birther" movement that falsely claimed Mr Obama was not born in the US, first responded with feigned exasperation - "We need the question", he said, to laughs - but let the man continue.

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".

Mr Trump's questions about the president's country of birth helped build his stature among some conservative voters and pushed Mr Obama to release a copy of his birth certificate in 2011. But the billionaire businessman has distanced himself from the issue during his current run.

Democratic presidential candidate Hillary Clinton said Mr Trump should disavow the comments about Mr Obama and Muslims.

She tweeted: "Donald Trump not denouncing false statements about POTUS (president of the United States) & hateful rhetoric about Muslims is disturbing, & just plain wrong. Cut it out."