Carson, a retired neurosurgeon, said last week, "I would not advocate that we put a Muslim in charge of this nation." The comment drew criticism from both Republicans and Democrats.
On Sunday, Tapper asked Carson about his comments.
"I would have problems with somebody who embraced all the doctrines associated with Islam," Carson said. "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."
Tapper and Carson spent several minutes of back and forth.
"You're assuming that Muslim Americans put their religion ahead of the country," Tapper said to Carson.
"I'm assuming that if you accept all the tenets of Islam that you would have a very difficult time abiding under the Constitution of the United States," Carson replied.
The conversation ended when a voice off-camera, which CNN identified as Carson's campaign manager, Armstrong Williams said, "This interview is over."
Watch the full interview from CNN: