WASHINGTON -- A leading Republican presidential candidate says he doesn't believe that a Muslim should be elected to the nation's top office, stirring up yet another controversy for a party that professes a commitment to broaden its appeal and promote tolerance.

Presidential candidate Ben Carson, a devout Christian, says a president's faith should matter to voters if it runs counter to the values and principles of America. Responding to a question during an interview broadcast Sunday on NBC's "Meet the Press," the retired neurosurgeon described the Islamic faith as inconsistent with the U.S. Constitution.

"I would not advocate that we put a Muslim in charge of this nation," Carson said in an interview aired Sunday on NBC's "Meet the Press." "I absolutely would not agree with that." He did not specify in what way Islam ran counter to constitutional principles.

Carson has been picking up support by appealing to socially conservative evangelical voters, a key Republican voting bloc in the Iowa caucuses which lead off the state-by-state nominating contests next year.

Republican leaders had hoped that the 2016 would provide an opportunity to make a fresh pitch to minorities, gays, women and others beyond the party's traditional core supporters.

After a blistering examination of the 2012 election, a report commissioned by Republican National Committee Chairman Reince Priebus concluded that "if our party is not welcoming and inclusive, young people and increasingly other voters will continue to tune us out."

But it hasn't unfolded according to the leadership's hoped-for script, with some high-profile candidates inviting lots of eyebrow-raising. Just in the past few days, their comments have underscored that the problems extend beyond Republicans' well-documented troubles appealing to Hispanics.

To be sure, former Florida Gov. Jeb Bush and several other candidates have disavowed some of that rhetoric or tried to stake out more moderate positions. It can be tough, though, to avoid getting drowned out by language sure to stir up people.

Front-runner Trump declined to correct a town hall participant who wrongly said President Barack Obama was a Muslim. Days later, Carson spoke about Muslims and the presidency -- remarks described as "un-American," by a spokesman for the Council on American-Islamic Relations, Ibrahim Hooper. Hooper said the Constitution expressly bars religious tests for those seeking public office.

"To me this really means he is not qualified to be president of the United States," Hooper said. "You cannot hold these kinds of views and at the same time say you will represent all Americans, of all faiths and backgrounds."

The rhetoric has provided an opening that Democrats are ready to try to exploit.

"Of course a Muslim, or any other American citizen, can run for president, end of story." said Rep. Debbie Wasserman Schultz, who leads the Democratic National Committee. "To think otherwise is not only harmful to our political process, but it elevates and validates discrimination in this country."