Republican presidential hopeful Ben Carson Benjamin (Ben) Solomon CarsonBiden cannot keep letting Trump set the agenda The Hill's 12:30 Report: Trump heads to New Hampshire after renomination speech Five takeaways on GOP's norm-breaking convention MORE is standing by his view that a Muslim should not be president of the United States, telling The Hill in an interview on Sunday that whoever takes the White House should be “sworn in on a stack of Bibles, not a Koran.”

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Carson ignited a media firestorm in a Sunday morning interview with Chuck Todd on "Meet the Press," in which he said he “would not advocate that we put a Muslim in charge of this nation.”

“I absolutely would not agree with that,” Carson said.

In an interview with The Hill, Carson opened up about why he believes a Muslim would be unfit to serve as commander in chief.

“I do not believe Sharia is consistent with the Constitution of this country,” Carson said, referencing the Islamic law derived from the Koran and traditions of Islam. “Muslims feel that their religion is very much a part of your public life and what you do as a public official, and that’s inconsistent with our principles and our Constitution.”

Carson said that the only exception he’d make would be if the Muslim running for office “publicly rejected all the tenets of Sharia and lived a life consistent with that.”

“Then I wouldn’t have any problem,” he said.

However, on several occasions Carson mentioned "Taqiyya," a practice in the Shia Islam denomination in which a Muslim can mislead nonbelievers about the nature of their faith to avoid religious persecution.

“Taqiyya is a component of Shia that allows, and even encourages you to lie to achieve your goals,” Carson said.

Pushing back at the media firestorm over his remarks, Carson sought to frame himself as one of the few candidates running for president willing to tell hard truths.

“We are a different kind of nation,” Carson said. “Part of why we rose so quickly is because we wouldn’t allow our values or principles to be supplanted because we were going to be politically correct. … Part of the problem today is that we’re so busy trying to be politically correct, that we lose all perspective.”

Carson told The Hill that the question of a Muslim president is largely “irrelevant” because no Muslims are running in 2016. He said the question, which Todd is posing to all of the Republican presidential hopefuls who go on his show, “may well have been” gotcha journalism meant to trip the candidates up.

However, he acknowledged the question “served a useful purpose by providing the opportunity to talk about what Sharia is and what their goals are.”

“So often we get into these irrelevant things, because obviously if a Muslim was running for president, there would be a lot more education about Sharia, about Taqiyya," Carson said.

The issue burst onto the scene last week when GOP front-runner Donald Trump declined to correct a questioner at a campaign rally who declared that President Obama is a Muslim.

Carson said that if put in the same situation, he would have corrected the person at the rally.

“I certainly would not have accepted the premise of a question like that,” Carson said.

However, the retired neurosurgeon declined to criticize Trump, saying those kinds of on-the-spot moments can be difficult to handle in the heat of the moment.

“[Trump] may not have been ready for that,” Carson said. “I can tell you from experience a lot of these things are much easier when you’re quarterbacking from the armchair the next day.”