Republican presidential front-runner Donald Trump began his campaign rally Thursday in New Hampshire by taking questions from the crowd.

The first questioner called US President Barack Obama a Muslim, accused him of not being an American, and asked Trump when America can get rid of Muslim "training camps" in the US.

"We have a problem in this country — it's called Muslims," the man said. "We know our current president is one."

To this, Trump responded, "right."

The man continued: "You know he's not even an American — birth certificate, man!"

"We need this question, this is the first question," Trump responded with nervous laughter.

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

Trump responded by steering clear of the question entirely and giving a vague catch-all statement before quickly calling for another question.

"We're going to be looking at a lot of different things, and a lot of people are saying that and saying that bad things are happening out there. We're going to be looking at that and plenty of other things," Trump said.

Allegations of Muslim "training camps" within the US has long stirred suspicion on the right. The far-right publication World Net Daily, for example, has alleged that the FBI has knowledge of more than 20 such "training camps" within the US. Some of those allegations have found their way into more mainstream media.

Trump's response to the New Hampshire man's questions looks like classic off-the-cuff damage control, but it does raise issues for a campaign already frequently immersed in controversy.

Trump did not correct the blatant falsehood that Obama is a Muslim, nor did he address the questioner calling American Muslims "a problem."

Trump released a statement to The Washington Post defending his comments.

"The media wants to make this issue about Obama," he told the Post. "The bigger issue is that Obama is waging a war against Christians in this country. Their religious liberty is at stake."

His campaign manager, Corey Lewandowski, talked to the Post late Thursday night to further defend Trump's answer.

"Mr. Trump was asked about training camps," Lewandowski said. "Mr. Trump answered the question and said, 'If there are any, we will fix it.' He said, 'I will look into it.' The question was specifically about training camps."

When asked if Trump believes that Obama is a Muslim, Lewandowski told the Post that he doesn't speak for Trump and that it's "up to the media" if they want to "make this about Obama."

Democratic presidential front-runner Hillary Clinton slammed Trump's comments in a tweet Thursday night:

Donald Trump not denouncing false statements about POTUS & hateful rhetoric about Muslims is disturbing, & just plain wrong. Cut it out. -H — Hillary Clinton (@HillaryClinton) September 18, 2015

The episode calls to mind that Trump was and still is a "birther," despite the White House releasing Obama's birth certificate four years ago. Trump said as recently as July that he doesn't know if Obama was born in the US.

Of course, this may not be an issue with Trump's supporters, many of whom, according to recent polls, do believe that the president is a Muslim who was born outside the United States.

Brett LoGiurato contributed to this report.