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Ben Carson said Monday he could indeed support a Muslim for president – despite words to the contrary on Sunday – should they pledge fealty to the Constitution.

Carson, under fire for seeming to suggest that he couldn’t support anyone who subscribes to Islam to lead the White House, issued a caveat to that position on Monday evening. In an interview with Fox News’ Sean Hannity, the Republican presidential candidate said there are some Muslims who could be president if they effectively renounced their faith.

“If someone has a Muslim background and they’re willing to reject those tenets and to accept the way of life that we have and clearly will swear to place our Constitution above their religion … I would then be quite willing to support them,” he said.

In a post on Facebook also on Monday night, Carson reiterated that position.

“I could never support a candidate for President of the United States that was Muslim and had not renounced the central tenant of Islam: Sharia Law,” he wrote. “I know that there are many peaceful Muslims who do not adhere to these beliefs. But until these tenants are fully renounced…I cannot advocate any Muslim candidate for President.

Carson, who made the initial remark on Sunday, told Hannity that his focus on radical Islamic beliefs was “implied in the comment.”

“I don’t care what religion or faith someone belongs to,” Carson said. “If they’re willing to subjugate that to the American way and to our Constitution, then I have no problem with that.”

Before Carson appeared on Hannity to clarify his remarks, a presidential candidate who had his own faith scrutinized as a potential barrier for fitness of office swiped at Carson’s statement.

“Of course, no religious test for the presidency – every faith adds to our national character,” tweeted Romney, who is Mormon.

Muslim-American group calls on Carson to drop out

Florida Sen. Marco Rubio, who also appeared on Fox News Monday night, also defended Muslim Americans’ right to political office.

“I personally know, first of all, that there are Americans that are Muslims and that are also very patriotic and they love the United States of America and they don’t want to see any Sharia law and they don’t want to see anything like that happen in this country,” he told Fox’s Hannity. “I don’t believe anyone should be disqualified from the presidency because of their denomination or because of their faith. I believe in that strongly.”

Opinion: The Republicans’ Muslim ‘problem’

Rubio said if someone did believe in Sharia law, they wouldn’t be elected anyway.

“But I do believe there are hundreds of thousands – if not millions – of people in this country who are Muslim but love America … they aren’t political about their religious views with regards to that the way you would see in some other countries around the world,” he said.

Clinton aide blasts Carson’s Muslim comments