Carson’s discussion with Meet the Press host Chuck Todd centered around controversy that arose this week when Donald Trump – the real-estate mogul keeping Carson in second place in the polls – failed to correct an audience member at a New Hampshire campaign rally who said President Obama was a Muslim.
The audience member also appeared to advocate the forcible removal of Muslims from the US.
On Saturday, in a series of tweets on the subject, Trump defended himself and said: “Am I morally obligated to defend the president every time somebody says something bad or controversial about him? I don’t think so!”
He also addressed the issue in an appearance before an evangelical audience in Iowa, at which he brandished a Bible and said: “You see, I’m better than you thought.”
In such circles, Trump has lost some support to Carson.
In his NBC interview, Carson was asked: “So do you believe that Islam is consistent with the constitution?”
“No,” he said, “I don’t, I do not.”
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.”
The first amendment to the constitution begins: “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof …”
Carson, a Christian, is a member of the Seventh Day Adventist Church. In October, he will publish a new book, written with his wife Candy Carson and entitled A More Perfect Union: What We the People Can Do to Reclaim Our Constitutional Liberties.
In publicity material issued by Penguin Random House, Carson is quoted as saying: “I believe that making a difference starts with understanding our amazing founding document, the US Constitution.
“And as someone who has performed brain surgery thousands of times, I can assure you that the Constitution isn’t brain surgery.
He adds that he and his wife wrote the book to “help defend” the constitution “from those who misinterpret and undermine it”.
Related: Quiet rise of Ben Carson is shaking up Republican presidential race
The Ohio governor John Kasich, who is polling an average of 2.5%, enough for 10th place out of 16, was also asked by NBC if he “would ever have a problem with a Muslim becoming president”.