Donald Trump
Audience members raise their hands to ask U.S. Republican presidential candidate Donald Trump a question at a campaign town hall meeting in Rochester, New Hampshire September 17, 2015.REUTERS/Brian Snyder

Republican presidential candidate Donald Trump has come under fire from members of his own party, as well as prominent Democrats, after failing to correct a supporter who said US President Barack Obama was a Muslim and not American.

The businessman, who is also the frontrunner for the Republican nomination, was at a campaign rally in New Hampshire on Thursday night (17 September) when he was asked a question by the unidentified man. "We have a problem in this country. It's called Muslims," the supporter said to Trump when he was called upon to ask a question. "We know our current president is one. You know he's not even an American."

Trump did not correct the man's claims and instead said he had heard others bring up the same issue. Fellow Republican presidential candidate and New Jersey Governor Chris Christie condemned his response on Friday (18 September), telling the Today Show that leaders have an "obligation" to correct erroneous statements. "If somebody at one of my town hall meetings said that, I would correct them and I would say, 'The president's a Christian and he was born in this country. Those two things are self-evident,'" he said.

Another Republican, South Carolina Senator Lindsey Graham, also agreed the businessman had acted inappropriately and called for him to apologise. "He's playing into this hateful narrative and he has to set it right," Graham told an interviewer on Friday.

Meanwhile, Democratic frontrunner Hillary Clinton condemned Trump's omission, tweeting shortly after the rally that his failure to denounce "hateful rhetoric" was "disturbing and wrong". Vermont Sen. Bernie Sanders - who is also seeking the Democratic presidential nomination - called upon Trump to apologise to the president and the American people for "continuing the lie that the president is not an American and not a Christian."

The White House also responded to the controversy, with spokesman Josh Earnest saying: "Mr Trump isn't the first Republican politician to countenance these views to gain votes."

In a statement, Trump's campaign said he was only acknowledging the man's inquiry. "The media wants to make this issue about Obama," it said. "The bigger issue is that Obama is waging a war against Christians in this country. Christians need support in this country. Their religious liberty is at stake."

Trump has questioned Obama's background in the past. In 2011, he launched a campaign calling for the president to release his birth certificate. The president released a copy of the certificate - confirming his place of birth is Hawaii.