Ben Carson
U.S. Republican candidate Dr. Ben Carson speaks during the Heritage Action for America presidential candidate forum in Greenville, South Carolina September 18, 2015. REUTERS/Chris Keane

Republican presidential candidate Ben Carson has continued to stand by his comments on Muslims and lists the pre-requisites for them to stand as US president. In a new interview with CNN, Carson went a step further and said Muslims should denounce the Quran to have his support.

"I would have problems with somebody who embraced all the doctrines associated with Islam," Carson told CNN's Jake Tapper. "If they are not willing to reject sharia and all the portions of it that are talked about in the Quran. If they are not willing to reject that, and subject that to American values and the Constitution, then of course, I would."

The GOP candidate, who has seen a rise in the polls, continued: "I would ask you, would you be willing to do that? Would you be willing to advocate for somebody who would not do that? Probably not." Doubling down, Carson added: "Is it possible that maybe the media thinks it's a bigger deal than the American people do? Because American people, the majority of them, agree and they understand exactly what I am saying."

The retired neurosurgeon came under fire earlier in September after telling NBC's Meet the Press: "I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that."

Carson continued: "I guess it depends on what that faith is. If it's inconsistent with the values and principles of America, then of course it should matter." The Seventh-day Adventist Church member said he did not believe Islam was consistent with the US Constitution. His campaign later attempted to clarify that he does not believe the American people were prepared to have a Muslim president.

The Republican presidential hopeful also used his interview on CNN to comment on Speaker John Boehner's shocking resignation on 25 September. "I think Speaker Boehner had a long and distinguished career," he said. "He's being pulled in a lot of different directions, tends to be a nice guy, and is a compromiser at a time when a lot of people on the right feel that too much compromise has already resulted in a situation that they're not very happy with."

A recent NBC/WSJ poll reveals Carson has shown a steady improvement in popularity, now trailing Republican front-runner Donald Trump by just one point, 21% to 20%.