During a rally in New Hampshire on Thursday evening, Donald Trump did not challenge an audience member who said that President Obama is Muslim and "not even an American." Trump was also asked what he would do to get rid of Muslim "training camps" and responded: "We're going to be looking at a lot of different things."

The exchange came during a post-debate rally in Rochester, N.H., during which Trump asked the audience for questions rather than giving a speech. To kick things off, Trump pointed at a man in the audience: "Okay, this man. I like this guy."

"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. Birth certificate, man."

"Right," Trump said, then adding with a shake of his head: "We need this question? This first question."

"But any way," the man said. "We have training camps... where they want to kill us."

"Uh huh," Trump said.

"That's my question: When can we get rid of them?" the man said.

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

Fears of "Muslim training camps" have simmered on the far right for years, especially since the rise of the Islamic State. World Net Daily and Judicial Watch -- the latter an advocacy group that has successfully sued for records from Hillary Clinton's tenure at the State Department -- have published stories that allege FBI knowledge of dozens of camps, many across the deep South. Trump is not the first Republican candidate to be asked about the reports, though his response -- that they may be worth looking into -- is unique.

As social media lit up with criticism of these comments on Thursday night, Trump responded in a statement to The Post: "The media wants to make this issue about Obama. The bigger issue is that Obama is waging war against Christians in this country. Their religious liberty is at stake."

Update, 9:55 p.m.: In an interview late Thursday with The Washington Post, Trump campaign manager Corey Lewandowski said, "Mr. Trump was asked about training camps. 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.

"The media wants to make this issue about Obama. The bigger issue is that Obama is waging a war against Christians in this country. They need support and their religious liberty is at stake," he added.

When asked whether Trump agrees with the questioner and believes that President Obama is a Muslim, Lewandowski said, "I don’t speak for Mr. Trump." He said "it’s up to the media" if they "want to make this about Obama."

After a town hall in Las Vegas, Sen. Rand Paul (R-Ky.) said he'd "never heard of anything like camps" for terrorists thriving in America while the government looked away.

"I would say that we have to be vigilant for those who have come into our country, particularly from the Middle East," Paul said. "And I am for increased scrutiny of those who visit us, and I am for increased scrutiny of those who visit us from certain countries that do have camps overseas. There's probably about 25 countries -- if someone wants to immigrate here from Yemen tomorrow, I think there should be a certain amount of scrutiny of that person. Same for Syria, same for Iraq, same for Iran, same for Pakistan."

Meanwhile, Democrats pounced on Trump's comments. "GOP frontrunner Donald Trump's racism knows no bounds," Democratic National Committee chair Debbie Wasserman Schultz said in a Thursday night statement. "This is certainly horrendous but unfortunately unsurprising given what we have seen already. The vile rhetoric coming from the GOP candidates is appalling."

Wasserman Schultz also said that all Republican presidential candidates who did not denounce Trump's comments immediately "will be tacitly agreeing with him.”

11:10 p.m.: Hillary Clinton weighed in.

Robert Costa and David Weigel contributed to this report.