Republican presidential candidate Ben Carson speaks at a health care summit September 18, 2015.

Republican presidential hopeful Ben Carson said no Muslim should be president of the United States, adding a new twist to a controversy roiling the party’s White House nominating race.

In an interview with NBC’s “Meet the Press,” Carson, a retired brain surgeon who often refers to his own deep Christian faith, was asked whether a president’s religion should matter.

“I guess it depends on what that faith is. 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,” he said.

Asked whether he believes Islam is consistent with the U.S. constitution, he responded: “No, I don’t. I do not.”

“I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that,” he added.

The Council on Islamic-American Relations said Carson’s comments make him unfit to be president.

“This disqualifies him from being a president,” CAIR director Nihad Awad said.

“My advice to GOP presidential candidates: Read the U.S. constitution if you haven’t yet! It keeps America great.”

A Carson campaign official later suggested Carson’s comments were being overstated and that Carson would likely reach out to the Muslim community, NBC reported.

“He did not say that a Muslim should be prevented from running, or barred from running in any way,” Carson campaign spokesman Doug Watts was quoted as saying by NBC.

“He (Carson) just doesn’t believe the American people are ready for that.”

The issue abruptly surfaced in recent days when Republican frontrunner Donald Trump let pass unchallenged a questioner’s assertion that U.S. President Barack Obama was a Muslim.

Carson, who slipped to third among Republican presidential contenders in opinion polls Sunday after running second to Trump for weeks, said he believed Obama was born in the United States and is a Christian.