Story highlights Trump also was asked about terrorist "training camps" and when the U.S. can "get rid" of Muslims

"We're going to be looking at a lot of different things," Trump replied

Washington (CNN) Donald Trump came under fire Friday morning for his handling of a question at a town hall about when the U.S. can "get rid" of Muslims, for failing to take issue with that premise and an assertion that President Barack Obama is Muslim.

Trump, who has shaken off several high-profile controversies that would have ended other presidential campaigns, faced an immediate backlash from advocacy groups, and members of his own party distanced themselves from the GOP front-runner. The incident recalls Trump's 2011 quest to challenge Obama on where he was born, which ended with Obama releasing his long-form birth certificate. It also follows a debate performance Wednesday that garnered mixed reviews for the billionaire businessman.

"We have a problem in this country. It's called Muslims," an unidentified man who spoke at a question-and-answer town hall event in Rochester, New Hampshire asked the mogul at a rally Thursday night. "You know our current president is one. You know he's not even an American."

A seemingly bewildered Trump interrupted the man, chuckling, "We need this question. This is the first question."

"Anyway, we have training camps growing where they want to kill us," the man, wearing a "Trump" T-shirt, continued. "That's my question: When can we get rid of them?"

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