Story highlights Carson clarified that his concern is that the president prioritize the U.S. Constitution over his or her faith

"I don't care what a person's religion beliefs are or religious heritage is," Carson said Tuesday

Washington (CNN) Ben Carson is changing his position on whether Muslims are fit to be president.

After sparking a controversy over the weekend by saying he doesn't think a Muslim should be in the White House, the Republican presidential contender said Tuesday that he is more interested in the president prioritizing the U.S. Constitution over his or her faith.

"I don't care what a person's religion beliefs are or religious heritage is," he said at a news conference in Sharonville, Ohio. "If they embrace our Constitution and are willing to place that above their religious beliefs, I have no problem with that."

That's a significant shift from Sunday when, during an appearance on "Meet the Press," NBC's Chuck Todd asked Carson, "Do you believe that Islam is consistent with the Constitution?"

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