Media playback is unsupported on your device Media caption Ben Carson: "I would not advocate that we put a Muslim in charge of this nation"

US Republican presidential hopeful Ben Carson says he does not believe a Muslim should become president.

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

The retired neurosurgeon has been running high in the polls.

It follows widespread condemnation of Republican frontrunner Donald Trump's failure to correct a supporter who said President Barack Obama was a Muslim.

But Mr Trump, who has come under pressure from both Democrats and Republicans to apologise, says it was "not his job" to defend President Obama.

Analysis: Laura Bicker, BBC News, Washington

Does a president's faith matter? Well yes if you're fighting to be a Republican nominee. This is a battle for an evangelical base, especially in the key state of Iowa. Donald Trump has come on stage with his bible.

Now Ben Carson seems to be suggesting that being a Muslim is essentially unAmerican. A recent survey suggests those who vote Republican or even lean towards the party have negative views of Muslims.

Asked to rate a series of religious groups on a "feeling thermometer" from zero (the coldest) to 100 (the warmest), Republicans gave Muslims an average of 33. The average rating among Democrats was a more neutral 47.

In a separate poll earlier this year more than half of Americans said they had unfavourable views of Islam.

Should a president's faith matter? Well not according to the US Constitution which states that "no religious test shall ever be required as a qualification to any office or public trust under the United States".

One of the business mogul's main opponents, Ben Carson, hit the headlines on Sunday after he told NBC TV that Muslims were unfit to be president.

He said he believed the president's faith should be consistent with the US constitution. Asked if he considered Islam to be consistent, he said: "No, I do not."

Mr Trump faced mounting criticism last week for failing to challenge a comment by one of his supporters, who said President Obama "was a Muslim" and "not even American".

The man also went on to say: "We have a problem in this country - it's called Muslims."

Media playback is unsupported on your device Media caption A history of calling Barack Obama a Muslim

President Obama, who has spoken openly about his Christian faith, was born to an American mother and Kenyan father in Hawaii.

But Mr Trump has been one of the leading sceptics, challenging Mr Obama in 2011 to produce his birth certificate to disprove rumours that he was born in Kenya, which the president did.

Ben Carson was asked in the NBC interview on Sunday whether he thought President Obama was born in the United States and is a Christian, to which he responded: "I believe that he is. I have no reason to doubt what he says."

One of the latest polls, run by CNN/ORC, shows Mr Carson has slipped into third place in the Republican race, trailing behind former Hewlett-Packard chief Carly Fiorina in second place and Mr Trump, who has consistently remained ahead of the pack.