Carson: I was taken out of context. (Photo by Sean Rayford/Getty Images)

SHARONVILLE, Ohio — GOP presidential candidate Ben Carson dismissed the idea that he is prejudiced against Muslims, insisting Tuesday during a news conference here that his statement Sunday that he would not support a Muslim for president was taken out of context.

“I don’t care what a person’s religious beliefs are or what their religious heritage is. If they embrace American culture, if they embrace our constitution and are willing to place that above their religious beliefs, I have no problem with it,” Carson said before a rally in Sharonville.

The retired neurosurgeon said his initial comments — which came during an interview that aired Sunday on NBC's "Meet the Press" — were not about Muslims broadly but about radical Islam and religious radicals of other faiths. “It’s on the record on NBC. On 'Meet the Press.' Did anyone pick up on that? Of course not, because that wasn’t the juicy story,” Carson told reporters.

“If the question had been asked about a Christian and they had said, you know, would you support a Christian who believes in establishing a theocracy, I would have said no,” he said.

Carson has spent the first part of the week dealing with the fallout from those comments. On Monday, he began to revise his weekend remarks, telling Fox News he would be prepared to accept a moderate Muslim candidate who denounced radical Islam. Those candidates “will be considered infidels and heretics, but at least then I will be quite willing to support them.”

Still, he defended his original position, telling Fox host Sean Hannity that the United States could not have leaders whose religion might conflict with constitutional principles.

“If you’re a Christian and you’re running for president and you want to make this into a theocracy, I’m not going to support you. I’m not going to advocate you being the president,” he said.

Carson's campaign has been greatly boosted by a profound anti-Washington sentiment throughout the country, which has elevated political outsiders like himself and business mogul Donald Trump to the top of the GOP field. As a candidate, the soft-spoken retired neurosurgeon provides a striking contrast to the flamboyant front-runner, even as they both run on similar anti-Washington rationales. And his message has considerable strength — a recent CBS/New York Times poll showed Carson surging just behind Trump, taking 23 percent support to the businessman's 27 percent.

"What resonates with people is that he is genuine, he is resolute, he stands firm on his beliefs. His message speaks to my values and my faith," said Jeremy Long, of Milford, Ohio, one of about 500 supporters who attended Carson's rally in Sharonville. Long added that he believes Carson's calls for "revival" and "healing" are resonating with many voters.

"This is my first political event I've ever been. I came to hear him myself in person. I loved everything he had to say," said Lindy Powell, who lives in the Cincinnati area. "With people that have faith, we really feel like the hand of God has been with him."

When asked about Carson's comments about not supporting a muslim for president, many attendees said that they shared Carson's concerns that a Muslim-American president would not be able to separate his or her faith from their mandate to protect the constitution. Many voters brought up the fear that a Muslim president would lie about his or her positions on issues in order to reach higher office. And those voters are not in the minority  — a Gallup poll earlier this summer found that more than half the Republicans surveyed would not vote for a well-qualified nominee who shared their political affiliation if that person were Muslim.

"I don't think a Muslim president would work. But the beautiful thing about this country is that they are free to practice their faith. He doesn't want to take that away," said Powell.
Following criticism for his remarks on "Meet the Press," Carson has forcefully stated repeatedly in recent days that he believes the presidential candidates must put the constitution before their faith, responding to questions about same-sex marriage, the Kim Davis controversy and abortion rights by saying that laws must be upheld and followed.

"If you’re not willing to do that, you should not be running for president. We have to live within the framework," Carson told reporters. "It doesn’t mean we can’t work to change it from within the system, but there are appropriate ways to do that."