|Mr Ben Carson.|
Calls are growing for Republican Ben Carson to quit the 2016 raceafter he said a Muslim should not be president.
Muslim-American groups, among others, have said these views make him unqualified to run himself.
Mr Carson, a Christian, made the comments on Sunday, adding that Islam was inconsistent with the Constitution.
Another Republican presidential candidate, Bobby Jindal, said on Monday a Muslim president should swear on a Bible to uphold the Constitution.
He said a Muslim Republican who fought to protect religious liberty, respected the Judeo-Christian heritage of the US and was committed to destroying Islamic State and radical Islam, and condemned cultures that treated women as second class citizens would get his vote.
But they must "place their hand on the Bible and swear to uphold the Constitution", he added.
The Republican candidates for president are being asked about their views on Islam since Donald Trump failed last week to correct a supporter who said President Barack Obama was a Muslim.
Mr Trump, the Republican frontrunner, has since said he would have no problem appointing a Muslim to his cabinet.
But in an interview with NBC's Meet the Press, Mr Carson said the president's faith matters if it differs with the values of America.
"I would not advocate that we put a Muslim in charge of this nation," he said.
He elaborated later when he told The Hill: "Muslims feel that their religion is very much a part of your public life and what you do as a public official, and that's inconsistent with our principles and our Constitution."