Presidential candidate Donald Trump has come under fire for failing to correct or rebuke a man who asked the presidential candidate a series of anti-Muslim questions.

The billionaire real-estate mogul and reality TV host was taking questions from the audience at a rally in New Hampshire when the man was chosen.

"We have a problem in this country. It's called Muslims," the man said.

"We know our current president is one. You know he's not even an American."

Trump cut in briefly to comment: "We need this question. This is the first question."

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

Trump has been criticised for his non-committal response.

"We’re going to be looking at a lot of different things," he told the rally.

"A lot of people are saying that and a lot of people are saying that bad things are happening out there."

Rival presidential contender Hillary Clinton has condemned Trump's response over Twitter.

Despite many accusations otherwise, President Obama was born in the United States and has repeatedly affirmed his Christian faith.

Later on the Trump campaign issued a statement attributed to the billionaire.

"The media wants to make this issue about Obama," the statement read.

"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's response stands in stark contrast to a similar accusation levelled against Barack Obama when he was first running for president in 2008.

Republican nominee John McCain took the microphone back from an audience member when she called him an "Arab".

"No ma'am, he's a decent family man, citizen, that I just happen to have disagreements with on fundamental issues. And that's what this campaign is all about."

Trump is still well ahead of the rest of his Republican rivals four months before the first primary vote at the Iowa caucus.

Clinton meanwhile is still leading the Democratic field nationwide despite trailing in the early states of Iowa and New Hampshire.