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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.”

Ben Carson: U.S. shouldn’t elect a Muslim president

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?”

“No, I do not,” Carson responded. “I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that.”

But Carson told an audience in Cedarville, Ohio, he was “asked about who should be allowed to be President of the United States.”

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“And I said I think anybody, regardless of their religion, if they are willing to embrace the values and principles of America and our Constitution and subject their beliefs to the Constitution,” he said. “I have no problem with that at all. And that’s perfectly reasonable.”

After the Cedarville event, Carson maintained that he has held a consistent position, despite evidence to the contrary. He claimed Sunday he said as long as such a person remains true to American values, he would have no objection.

He initially walked back his comments on Monday, after receiving criticism from Democrats and Republicans alike.

In a post on Facebook on Monday night, Carson said a Muslim could serve as president if they disavow Sharia law in order to get his support.

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

CNN’s Joe Johns contributed to this report