Story highlights Rand Paul said that he would have no problem supporting a Muslim for president

Paul said voters would nevertheless have an "honest question" about Muslims seeking the highest office

Washington (CNN) Republican presidential candidate Rand Paul said Tuesday that he would have no problem supporting a Muslim for president -- and that Barack Obama isn't one.

In the aftermath of rival Ben Carson saying he wouldn't be able to support someone who subscribes to Islam to lead the country, the Kentucky senator said unequivocally that he believed the current president was born in the United States and is Christian. In the past, some other Republicans -- including GOP front-runner Donald Trump -- have at times publicly doubted the President's heritage and faith.

Paul said voters would nevertheless have an "honest question" about Muslims seeking the highest office.

"Do you believe literally that a woman should be stoned to death for adultery? Do you believe that when someone steals something, their hand should be cut off?" said Paul to CNN's Wolf Biltzer "The Situation Room."

Paul said he could back a Muslim "if they support the things that made America great -- constitutional principles, Bill of Rights -- but some of those are inconsistent with the interpretation of the Quran that's being put forward."

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