Washington: Republican presidential candidate Ben Carson said on Sunday that Muslims were unfit to be president of the United States, arguing their faith was inconsistent with American principles.

"I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that," Carson told NBC's "Meet the Press."

The remarks by Carson, who is near the top of opinion polls for the crowded field of Republican candidates, followed a controversy that erupted when front-runner Donald Trump declined to challenge anti-Muslim comments made by a supporter on Friday.

Carson, a Christian who says he got the idea for his tax proposals from the Bible, said he thought a US president 's faith should be "consistent with the Constitution. Asked if he thought Islam met this bar, the retired neurosurgeon said: "No, I do not."

America's largest Muslim civil rights group condemned Carson for his statement, which it said should disqualify him from the presidential contest because the US Constitution forbids religious tests for holding public office.

"It's beyond the pale and he should withdraw," said Council on American-Islamic Relations spokesman Ibrahim Hooper.

Minnesota Democratic Representative Keith Ellison, the first practicing Muslim elected to Congress, said: "It's unimaginable that the leading GOP presidential candidates are resorting to fear mongering to benefit their campaigns."