U.S. Republican presidential candidate Ben Carson, under fire for saying a Muslim should not be president, said on Monday he "absolutely" stood by his comments but would be open to a moderate Muslim candidate who denounced radical Islamists.
Carson, who is one of the top-polling Republican candidates, told NBC's "Meet the Press" on Sunday that he "would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that."
Saying he thought a president's faith should be "consistent with the Constitution," Carson, a Christian, said he did not believe Muslims met that bar.
Council on American-Islamic Relations Executive Director Nihad Awad has called on Carson to quit the presidential race "because he is unfit to lead, because his views are inconsistent with the United States Constitution."
See photos of Carson's 2016 campaign:
Ben Carson on the campaign trail
Republican candidate Carson 'absolutely' stands by comments on Muslims
MT. AYR, IA - JANUARY 22 : Republican presidential candidate Ben Carson is introduced during his 'Trust in God Townhall' campaign stop January 22, 2016 in Mt. Ayr, Iowa. Carson, who is seeking the nomination from the Republican Party is on the presidential campaign trail across Iowa ahead of the Iowa Caucus taking place February 1. (Photo by Joshua Lott/Getty Images)
Ben Carson, 2016 Republican presidential candidate, speaks during a Liberty University Convocation in Lynchburg, Virginia, U.S., on Wednesday, Nov. 11, 2015. As retired neurosurgeon Carson has risen in the polls, media reports have revisited his accounts of acts of violence as a child, a key part of the redemption story he discusses on the campaign trail. Photographer: Andrew Harrer/Bloomberg via Getty Images
PALM BEACH GARDENS, FL - NOVEMBER 06: Republican presidential candidate Ben Carson speaks to the media before speaking at a gala for the Black Republican Caucus of South Florida at PGA National Resort on November 6, 2015 in Palm Beach, Florida. Carson has come under media scrutiny for possibly exaggerating his background and other statements he has made recently. (Photo by Joe Raedle/Getty Images)
DES MOINES, IA - AUGUST 16: Republican presidential hopeful Ben Carson (L) eats a piece of pizza while touring the Iowa State Fair on August 16, 2015 in Des Moines, Iowa. Presidential candidates are addressing attendees at the Iowa State Fair on the Des Moines Register Presidential Soapbox stage and touring the fairgrounds. The State Fair runs through August 23. (Photo by Justin Sullivan/Getty Images)
LAKEWOOD, CO - OCTOBER 29: Republican presidential candidate Ben Carson speaks during a news conference before a campaign event at Colorado Christian University on October 29, 2015 in Lakewood, Colorado. Ben Carson was back on the campaign trail a day after the third republican debate held at the University of Colorado Boulder. (Photo by Justin Sullivan/Getty Images)
WASHINGTON, DC - SEPTEMBER 25: Scenes around the the Value Voters Summit on September 25, 2015 in Washington DC. Republican presidential candidate Ben Carson takes the stage at the event. Dr Carson speaks to the media after the speach. (Photos by Charles Ommanney/The Washington Post via Getty Images)
Attendees wait for Ben Carson, 2016 Republican presidential candidate, not pictured, to arrive during a campaign stop at the birthplace of the Michigan Republican Party in Jackson, Michigan, U.S., on Wednesday, Sept. 23, 2015. Carson, the third candidate in the Republican race to have never held elected office, saw his numbers drop following the debate last week. Photographer: Luke Sharrett/Bloomberg via Getty Images
Ben Carson, 2016 Republican presidential candidate, listens as he attends a service at Maple Street Missionary Baptist Church in Des Moines, Iowa, U.S., on Sunday, Aug. 16, 2015. Carson will be speaking at the Iowa State Fair, which is expected to host 18 presidential candidates and runs until Aug. 23. Photographer: Daniel Acker/Bloomberg via Getty Images
CLEVELAND, OH - AUGUST 06: Republican presidential candidate Ben Carson participates in the first prime-time presidential debate hosted by FOX News and Facebook at the Quicken Loans Arena August 6, 2015 in Cleveland, Ohio. The top-ten GOP candidates were selected to participate in the debate based on their rank in an average of the five most recent national political polls. (Photo by Chip Somodevilla/Getty Images)
Ben Carson, 2016 Republican presidential candidate, eats a slice of pizza as he tours the Iowa State Fair in Des Moines, Iowa, U.S., on Sunday, Aug. 16, 2015. In a Sunday interview with Fox News, Carson doubled down on his assertion that a speech given by President Barack Obama intended to sell the American public on his nuclear deal with Iran contained 'coded innuendos employing standard anti-Semitic themes.' Photographer: Daniel Acker/Bloomberg via Getty Images
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Carson's comments have also been criticized by some of his Republican rivals for president, who note that the Constitution makes clear there should be no religious test for office.
Asked on Fox News Channel's "Hannity" on Monday if he stood by his Muslim comments, Carson replied: "Absolutely."
"You know what we have to do is we have to recognize this is America and we have a Constitution and we do not put people at the leadership of our country whose faith might interfere with carrying out the duties of the Constitution," the retired neurosurgeon was quoted as saying in excerpts from the interview airing on Monday night.
But he added he would be open to the idea of a moderate Muslim who denounced radical Islamists as a candidate for president.
When asked if he had meant to say "radical Islamists" in his "Meet the Press" interview, Carson said: "It was implied in the comment because I prefaced that by saying I don't care what religion or faith someone belongs to, if they're willing to subjugate to the American way and to our Constitution then I have no problem with it."
For more on the 2016 presidential race, see the Reuters blog, "Tales from the Trail" (here).