The controversy over Republican presidential candidate Ben Carson’s declaration that no Muslim should be president of the United States escalated on Monday, as civil liberties groups and rival politicians registered their disapproval and an Islamic American relations advocacy group called for Carson to end his candidacy.

Critics said that Carson’s statement ran counter to the US constitution and to the American ideal, and that it bespoke a dangerous prejudice.

“Dr Carson’s statement directly contradicts the constitution and the values embodied in it,” said Jonathan Greenblatt, director of the Anti-Defamation League, in a statement. “In America, personal characteristics – whether race, sex, national origin, sexual orientation, gender identity or religion – should have no bearing on a person’s ability to serve.”

The Carson campaign, however, was refusing to back down, insisting that the candidate was giving his honest opinion without heed for political correctness.

Carson ignited the debate in an interview with NBC News host Chuck Todd, broadcast on Sunday. “I would not advocate that we put a Muslim in charge of this nation,” he said. “I absolutely would not agree with that.”

Ben Carson made the comments during an interview on NBC’s Meet the Press. Link to video

Carson told Todd that he did not think Islam was “consistent with the [US] constitution”.

The sweeping characterization of Islam was at odds with some previous statements Carson has made about the religion. In his 2012 book, America the Beautiful, which was co-authored with his wife, Candy, Carson describes a dinner conversation in which an unnamed “expert on Islamic culture” expresses doubts that Islam and Christianity can peacefully coexist.

“It is very important to remember, however, that there are 1.4 billion Muslims in the world,” the Carsons write, “and to paint them with a single philosophical brush is just as absurd as trying to characterize the diverse thinking of billions of Christians around the world.”

Multiple people with the Carson campaign did not respond to calls and emails for comment Monday. In an appearance on CNN early Monday morning, Carson business manager Armstrong Williams, the popular conservative radio host, said that Carson had been asked his opinion and given it without reservation.

“His opinion was, the timing at this point, he would not vote for a Muslim in the White House,” said Williams. “This is why he’s not a politician. This is why he’s not trying to be politically correct. This is America. It’s a place of freedom of speech. It is not an issue of religion, it is an issue of one’s belief system, of how they will govern.”

However, Carson’s claims about the Muslims and the White House drew an unusual intensity of censure on Monday from a diverse array of voices. Rival Republican candidates edged away from Carson’s comments, but held back from directly condemning the neurosurgeon, who has surged in the polls.

“The constitution provides that there should be no religious test for public office, and I’m a constitutionalist,” said Ted Cruz, the senator from Texas who also is running for the Republican nomination, when asked about Carson’s statement.

“Article VI of the constitution says there won’t be a religious test,” said Rand Paul, the Kentucky senator who is running for president, in a statement.

Article VI of the US constitution states: “No religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.”

Nihad Awad, founder and director of the Council on American-Islamic Relations (CAIR), called on Carson to withdraw from the presidential race and announced a campaign to give away free copies of the Quran. “We are providing copies of the Quran free of charge,” he said.

“The protection of freedom of religion in America is a fundamental principle of our country,” Awad said in a news conference. “Not long ago, some people thought that a Catholic cannot be a president, an African American cannot be a president. They were wrong then, and they are wrong now. And that is why we say that Ben Carson is wrong today to say that a Muslim cannot be president of the United States.”

Democratic National Committee chairperson Debbie Wasserman Schultz, the congresswoman from Florida, said in a statement that other Republicans had failed to distance themselves from views such as Carson’s.

“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,” she said. “Of course a Muslim, or any other American citizen, can run for president, end of story.”

Not every reaction to Carson’s statements was as critical. Louisiana governor Bobby Jindal, who also is running for president, called the Carson controversy “a dumb game that the press is playing” but then agreed in a statement to “play their gotcha game”.

“If you can find me a Muslim candidate who is a Republican, who will fight hard to protect religious liberty, who will respect the Judeo-Christian heritage of America, who will be committed to destroying Isis and radical Islam, who will condemn cultures that treat women as second-class citizens and who will place their hand on the Bible and swear to uphold the constitution, then yes, I will be happy to consider voting for him or her,” Jindal said.

“If you can’t, I’ll settle for voting for a Christian governor from Louisiana.”