For Republican presidential aspirant Ben Carson, a Muslim should never become president of the United States.

In an interview on NBC's "Meet the Press" on Sunday, Carson said the Islamic faith is not "consistent" with the US Constitution.

"If it's inconsistent with the values and principles of America, then of course it should matter, but if it fits within the realm of America and consistent with the Constitution, no problem," Carson said, when asked if a presidential candidate's faith should matter to the voters.

"I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that," he added.

Carson also said he is hoping that US President Barack Obama is really a Christian and an American.

However, the retired neurosurgeon said Muslims can be part of Congress. "It depends on who that Muslim is and what their policies are. Just as it depends on what anybody else says," Carson said.

"And if there's somebody who's of any faith but they say things and their life has been consistent with things that will elevate this nation and make it possible for everybody to succeed and bring peace and harmony, then I'm with them," he added.

Carson's remarks sparked outrage in the Muslim community, prompting his campaign spokesman, Doug Watt, to say that the Republican presidential aspirant will likely reach out to members of the Muslim community.

"He [Carson] did not say that a Muslim should be prevented from running, or barred from running in any way. He just doesn't believe the American people are ready for that," Watts said.

The topic of religion and the presidency came into the forefront after an unnamed man made controversial remarks during a forum with another Republican candidate, Donald Trump.

The man said Obama is a Muslim and is not a real American.

Although he drew flak for not correcting this remark, Trump earlier said that he has no problem with having a Muslim as an American president, saying he has "fabulous" friends who subscribe to the Islamic faith.

The outspoken business tycoon nevertheless said there is "a very severe problem" with some Muslims around the world.