Ben Carson is taking the edge off his controversial remarks that a Muslim should not be president, blunting his rhetoric to indicate that he would be comfortable with a moderate Muslim in the White House.

"If someone has a Muslim background, and they're willing to reject those tenets [of Sharia law] and to accept the way of life we have, and clearly will swear to place our Constitution above their religion," the 2016 hopeful said in a Monday night interview with Sean Hannity on Fox News Channel, "then I would then be quite willing to support them."

Carson has been dealing with severe blowback from Democrats, Muslim activist groups and even some of his Republican rivals for the presidential nomination, for saying in an interview on "Meet the Press" that he does not believe Islam is consistent with the Constitution and that he could not "advocate that we put a Muslim in charge of this nation."

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