Trump under fire again -- for something he di...

Updated with response from Donald Trump's campaign.

ROCHERSTER, N.H. - Republican presidential front-runner Donald Trump declined Thursday to correct a questioner at a 3,000 person rally who incorrectly stated that President Obama is Muslim and said he'd be "looking at" claims of terrorist training camps on American soil.

Trump, who has a history of making 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.

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

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Trump first interrupted, "We need this question--this is the first question?" he said, laughing. Trump, who was a driver of the "birther" movement that claimed Obama wasn't born in the U.S, let the man continue.

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

Trump did not dispute the man's assertions and said he'd heard others raise the issue.

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

The incident evoked a moment during the 2008 campaign when Republican nominee John McCain took the microphone away from a woman who said she didn't trust Obama because he was an "Arab."

Republican presidential candidate Donald Trump speaks at a town hall event Thursday, Sept. 17, 2015, in Rochester, N.H. AP Photo/Robert F. Bukaty

Trump's questions about the president's country of birth helped build his stature among some conservative voters and pushed 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.

After the event, Trump's campaign manager Corey Lewandowski called CBS News' Sopan Deb to assert that Trump's response, "I will look into that, we need to do something about that," referred only to the question about the training camps.

When asked why Trump didn't disavow the question, Lewandowski said, "I don't speak for Mr. Trump. He answered the question that was asked. He didn't hear the question basically. It was the first question, he couldn't even hear it and then he answered the question about training camps that he was asked."

And on whether he felt the question was appropriate, Lewandowski responded, "I don't speak for Mr. Trump."

The Trump campaign also released a statement attributed to "Mr. Trump," which read, "The media wants to make this issue about Obama. 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."

Hillary Clinton chastised Trump Thursday night, tweeting, "Donald Trump not denouncing false statements about potus & hateful rhetoric about muslims is disturbing, & just plain wrong. Cut it out."

CBS News' Jacqueline Alemany contributed to this report.