NEW YORK - The Islamic faith is not ‘consistent’ with the US Constitution, and a Muslim shouldn’t be president, Republican presidential candidate Ben Carson, an Afro-American neurosurgeon, has said.

“I would not advocate that we put a Muslim in charge of this nation,” Carson said on NBC’s Meet the Press on Sunday.

Carson said the religious beliefs of a president would matter if his or her faith was inconsistent with US values. His view contrasted with that of Donald Trump, the billionaire front-runner for the Republican presidential nomination, who said on the programme that a Muslim as president is something that could happen in the future.

Trump said he knows many Muslims who are “fabulous,” but there’s “a very severe problem” with some Muslims around the world - comments he repeated on other Sunday broadcasts.

The comments come after Trump failed to correct a man asking a question during one of his rallies on Sept. 17, who said that President Barack Obama is a Muslim. On “Meet the Press,” Trump said he wasn’t obligated to defend Obama.

“This is the first I’ve ever gotten into hot water for not saying anything,” Trump said. Trump and Carson both said they believe Obama is a Christian.

Meanwhile, Republican presidential front-runner Donald Trump has responded to a widening controversy over dodging a supporter's comment that Muslims pose a danger to the United States, saying: "I love the Muslims. I think they're great people." Trump made the comment after addressing high school students in Iowa at their homecoming Saturday night.

During a question-and-answer session with students, Trump was unable to avoid being asked about the latest political controversy dogging his campaign: his decision not to correct a supporter this week who called President Obama a Muslim.

One student told Trump that she considered Muslim-Americans to be an important segment of the country. They asked whether the billionaire businessman would consider putting a Muslim in his Cabinet or on his ticket. "Oh, absolutely," Trump responded. "No problem with that."

At a New Hampshire town hall on Thursday, a supporter stated that Obama was a Muslim and not American -which Trump did not correct - and asked the candidate how he plans to "get rid of" Muslim "training camps" in the country.

"We're going to be looking at a lot of different things," Trump responded. "You know, a lot of people are saying that and a lot of people are saying that bad things are happening."Trump has largely avoided the press since the flap. He canceled a South Carolina campaign event on Friday, citing business obligations, and chose to forego press gaggles at two events in Iowa on Saturday.

Under fire from critics for the interaction, Trump sent out a series of tweets Saturday, defending why he chose not to correct the supporter. "Am I morally obligated to defend the president every time somebody says something bad or controversial about him? I don't think so!" Trump wrote.

In another tweet, he said: "If I would have challenged the man, the media would have accused me of interfering with that man's right of free speech. A no win situation!"

Trump was noticeably subdued as he addressed a crowd of teenagers ahead of their dance on Saturday, advising them to stay away from alcohol and drugs and encouraging them to pursue professions they felt passionate about.