"I would not advocate that we put a Muslim in charge of this nation," the retired neurosurgeon said. "I absolutely would not agree with that."
Asked whether the faith of a president should matter, Carson, a practicing Christian, 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 stated.
The Council on American-Islamic Relations, the largest US Muslim civil rights and advocacy organization, condemned Carson over his controversial remarks.
"To me this really means he is not qualified to be president of the United States," said the organization`s spokesman, Ibrahim Hooper. "You cannot hold these kinds of views and at the same time say you will represent all Americans, of all faiths and backgrounds."
Carson`s comments came after frontrunner Republican presidential candidate Donald Trump did not respond to remarks made by a purported Trump supporter at a campaign.
The man wrongly called US President Barack a Muslim and said Muslims are "a problem in this country."
Trump has responded to criticisms, saying he was not obligated to correct the questioner.
In an interview on Sunday, Trump said that a Muslim in the White House is "something that could happen.
Asked whether he would be comfortable with a Muslim president of the United States. "Some people have said it already happened, frankly," Trump responded
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