Donald Trump is taking heat from both sides of the aisle after he declined Thursday to correct a questioner at a town hall event who incorrectly stated President Obama is Muslim, and "not even an American."

Trump was kicking off a town hall event in Rochester, N.H. -- 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." 

Trump, who was a driver of the "birther" movement that claimed Obama wasn't born in the U.S, first responded with feigned exasperation -- "We need the question," he said, to laughs -- but 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?" 

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Trump did not dispute the man's assertions and answered: "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. We're going to be looking at that and plenty of other things." 

After the exchange attracted widespread attention -- and criticism -- Trump released a statement saying the media want to make the 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," he said in a statement Friday. 

Democrats seized on the exchange, and Hillary Clinton tweeted that "Trump not denouncing false statements about POTUS & hateful rhetoric about Muslims is disturbing, & just plain wrong." 

New Jersey Gov. Chris Christie, a Republican presidential candidate, also said on NBC's "Today" show that he would have corrected anyone saying something like that at his town hall meetings. 

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." 

Trump's questions about the president's country of birth 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. 

Trump's town hall, in a sweaty auditorium in Rochester, was also interrupted several times by a protester, whose interruptions were met by hostility from the friendly crowd. 

The Associated Press contributed to this report.