In a rapid-fire series of tweets, the billionaire real estate mogul yesterday responded to a barrage of criticism of his handling of the Thursday incident, which came from Democrats and one fellow Republican candidate, New Jersey Governor Chris Christie.
"Am I morally obligated to defend the president every time somebody says something bad or controversial about him? I don't think so!" Trump wrote, ending an unusually long period of silence after he was largely quiet on Friday.
Trump, who helped fuel a "birther" movement in 2011 by repeatedly demanding Obama prove he wasn't born in Kenya, appeared to encourage a man at a campaign stop in New Hampshire Thursday after he made the incorrect assertion about Obama's faith.
"We have a problem in this country, it's called Muslims. We know our current president is one, you know he's not even an American," the unidentified questioner said.
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Putting himself in Trump's shoes, Christie said he would have corrected the questioner and said: "No, the president's a Christian and he was born in this country."
Hillary Clinton, the leading Democratic candidate, called Trump's handling of the incident "disturbing and just plain wrong," while White House spokesman Josh Earnest said it was no surprise because "the people who hold these views are part of Mr Trump's base."
Trump cancelled a campaign stop in South Carolina Friday after the flap broke.
But yesterday Trump did not back down, saying it was the first time in his life he had caused a controversy "by NOT saying something."
"If I would have challenged the man, the media would have accused me of interfering with that man's right of free speech.