Asked whether his faith or the faith of a president should matter, Carson said, "It depends on what that faith is."
"If it's inconsistent with the values and principles of America, then of course it should matter. But if it fits within the realm of America and consistent with the constitution, no problem," he explained, according to a transcript.
Todd then asked Carson, whose rise in the polls has been powered in large part by Christian conservatives, if he believed that "Islam is consistent with the Constitution."
"No, I don't, I do not," he responded, adding, "I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that."Carson said he would not necessarily have the same view about voting for a Muslim for Congress.