Carson campaign spokesman Doug Watts said Carson will likely reach out to members of the Muslim community in wake of the comments but said theinterview should be "watched or read carefully."
"He did not say that a Muslim should be prevented from running, or barred from running in any way," Watts said. "He [Carson] just doesn't believe the American people are ready for that."
Carson said Sunday in response to an interview question that "I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that."
When asked if a candidate's faith should matter to voters, Carson said, "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." When asked if he thought Islam is consistent with the Constitution, Carson said, "No, I don't, I do not."
Watts acknowledged that Carson's comments had generated controversy but said "this has taken on a little bit of a life of its own."
Check out photos of Ben Carson on the campaign trail:
Ben Carson on the campaign trail
Ben Carson's campaign responds to outrage over comments on Islam
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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"Dr. Carson is a strict adherent to the First Amendment — freedom of religion. That includes people of all faith," Watts said. "He has great respect for the Muslim community, but there is a huge gulf between the faith and practice of the Muslim faith, and our Constitution and American values.
"That can be disputed," Watts continued. "That can be debated. But there's pretty strong evidence to that effect."
The Council on American-Islamic Relations on Sunday called for Carson to withdraw from the race.
"Mr. Carson clearly does not understand or care about the Constitution, which states that 'no religious test shall ever be required as a qualification to any office,'" the group's national executive director, Nihad Awad, said in a statement.
Democratic presidential candidate Bernie Sanders said in a statement Sunday that "I am very disappointed that Dr. Carson would suggest that a Muslim should not become president of the United States."
"It took us too long to overcome the prejudice against electing a Catholic or an African-American president," he said in a statement. "People should be elected to office based on their ideas, not their religion or the color of their skin."
Carson's comments come days after another Republican presidential candidate, Donald Trump, did not distance himself from a questioner at a town hall meeting in New Hampshire who accused President Obama of being a foreign-born Muslim.
Carson said he has "no reason to doubt" that President Obama was born in the United States and is a Christian.
U.S. Rep. Keith Ellison, who was the first Muslim elected to Congress, accused both Carson and Trump of "fear mongering."
"For Ben Carson, Donald Trump, or any other Republican politician to suggest that someone of any faith is unfit for office is out of touch with who we are as a people," the Democrat from Minnesota said.
"It's unimaginable that the leading GOP presidential candidates are resorting to fear mongering to benefit their campaigns, and every American should be disturbed that these national figures are engaging in and tolerating blatant acts of religious bigotry," he said in a statement issued on Sunday.