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."
"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.
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"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."
"Donald Trump not denouncing false statements about POTUS (president of the United States) & hateful rhetoric about Muslims is disturbing, & just plain wrong. Cut it out," she tweeted.
Campaign manager Corey Lewandowski said that the room was noisy and that Trump had trouble hearing the question.
But the questioner was speaking into a microphone, and his remarks could be heard clearly by several journalists sitting near the back of the gymnasium.
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 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.