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WASHINGTON (CNN) -- Ben Carson said Sunday Muslims seeking public office must first renounce some central tenets of Islam. Otherwise, Carson said, "Why in fact would you take that chance?"

He also said he'd listen to arguments that religion should be reason for probable cause to track the emails and phone calls of Syrian refugees and others from the Middle East.

"I personally don't feel that way, but I would certainly be willing to listen to somebody who had evidence to the contrary," Carson said. "I think that's one of the problems, we get to our little corners and we don't want to listen to anybody."

The retired neurosurgeon and Republican presidential contender's comments in an interview with ABC's "This Week" host Martha Raddatz came the week after he'd said he "would not advocate that we put a Muslim in charge of this nation."

"I said anybody, doesn't matter what their religious background, if they accept American values and principles and are willing to subjugate their religious beliefs to our Constitution," Carson said. "I have no problem with them."

However, he said Muslims must renounce Sharia law.

"What we should be talking about is Islam and the tenets of Islam and where do they come from? They come from Sharia. They come the Koran. They come from, you know, the life works and examples of Mohammed. They come from the fatwas, which is the writings of scholars," Carson said.

"You know, and if you go back and you look at -- what I would like for somebody to show me is an improved Islamic text that opposes Sharia. Let me see -- if you can show me that, I will begin to alter my thinking on this," he said.

"But right now, when you have something that is against the rights of women, against the rights of gays, subjugates other religions, and a host of things that are not compatible with our Constitution, why in fact would you take that chance?"

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