The comments come as Carson has taken an increasingly aggressive stance toward Muslims, and a day after national Republican poll leader Donald Trump pledged he would support deporting Syrian Muslims.
"To bring into this country groups infiltrated with Jihadists makes no sense," Carson told about 150 at the Des Moines Rotary Club's monthly morning breakfast meeting. "Why would you do something like that?"
Instead, Carson recommended that the US help settle Syrian refugees in the Middle East, in places such as Turkey. In Carson's view, the US could assist financially, but not open its doors.
However, Carson has taken an increasingly skeptical view of Muslims in his public comments in recent days, as his political fortunes have improved. Carson now finds himself atop national Republican preference polls with Trump, and reported raising an impressive USD 20 million for his campaign in the third quarter of the year.
Carson has also launched a petition challenging the tax exempt status of the largest Muslim advocacy group, part of an escalating rift with the US Muslim community.
The Council on American-Islamic Relations last month called for Carson to quit the presidential race after he said a Muslim should not serve as president.
Carson has repeatedly warned that officials needed to carefully screen for potential terrorist ties Syrian refugees seeking to enter the United States, but went further today.
Despite anxiousness among some Republicans about the appearance of intolerance in a party trying to reach more minority voters, Carson's team has said publicly it works to his advantage in segments of the Republican electorate.