Republican presidential candidate Ben Carson stirred further debate on whether a Muslim can become U.S. president.

During an interview on NBC's "Meet the Press," Carson said a U.S. president's faith should matter to the electorate.

"It depends on what that faith is," Carson said. "If it's inconsistent with the values and principles of America, then of course it should matter. But if it fits within the realm of America and consistent with the Constitution, no problem."

When asked if he believes Islam is consistent with the U.S. Constitution, Carson said, "No.

"No, I do not. I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that," Carson said, adding the topic does differ if a Muslim seeks congressional office, but it depends on the individual.

The current GOP presidential front-runner may have been a bit more open-minded with the idea of a Muslim president. Also speaking to NBC News, Trump said, "It's something that at some point could happen. We'll see, it could happen. Would I be comfortable? I don't know if we have to address it right now but it is certainly something that could happen."

Democratic National Committee Chair Debbie Wasserman Schultz, congresswoman for Florida's 23rd Congressional District, said someone's religious beliefs should not disqualify him or her from being president.

"It's hard to understand what's so difficult about supporting an American citizen's right to run for president, but unsurprisingly, this left Republicans scratching their heads," Wasserman Schultz said in a statement. "Of course a Muslim, or any other American citizen, can run for president, end of story. To think otherwise is not only harmful to our political process, but it elevates and validates discrimination in this country."

The DNC chair said the Republican candidates should apologize and "state clearly where they stand."

Fellow Republican presidential candidate Ted Cruz, senator for Texas, steered clear from the debate. Cruz acknowledged that the Constitution specifies that no religion should effect an individual's right to run for public office. The Texas senator also said President Barack Obama's faith is "between him (Obama) and God" and added he will only focus on his public policy record.

Speaking to Iowa public television, Cruz said, "The Constitution specifies there shall be no religious test for public office, and I am a constitutionalist."

Louisiana Gov. Bobby Jindal, also running for the Republican presidential nomination, said the media is unnecessarily stirring debate on whether a Muslim can be U.S. president.

"This is a dumb game that the press is playing. It is an absurd hypothetical question, but let's indulge the media for a moment and play their gotcha game," Jindal said in a statement.

Jindal said if there is a Muslim Republican candidate who will protect religious liberty, respect Judeo-Christian heritage, commit to eliminate the Islamic State militant group and radical Islam, condemn cultures who treat women as second-class citizens and place his or her hand on the Bible and uphold the Constitution, then, "Yes, I will be happy to consider voting for him or her. ...

"If you can't, I'll settle for voting for a Christian governor from Louisiana."


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