Jowers said Romney is "incredibly data-driven" when it comes to hiring and makes decisions based on merit. "People in Utah who worked for Mitt at the Olympics know that the best person got the job and the best person got promoted, period," he said. Romney led the 2002 Winter Olympics in Salt Lake City.

Romney's initial remarks were surprising to Tarek Nosseir, president of the Islamic Society of Greater Salt Lake. He said Muslims living in Utah share a unique connection with their Mormon neighbors. "We share similar beliefs of family, social justice," Nosseir said. "It is hurtful to me that a person who is seeking the highest office in the nation is just not willing to put the best person in the job according their qualifications."

Both religions are minorities in the United States, and Romney has often found himself defending his faith as a member of the LDS Church, saying it shouldn't be a factor in his campaign.

Mormons comprise roughly 1.3 percent of the nation's adult population, according to a 2005 Baylor Religion Survey. Surveys place Muslims at less than 1 percent of adults, though some estimates suggest the Muslim population in the U.S. is 2 percent or more.

In the Monitor article, Ijaz wrote that Romney's apparent rejection of Muslims for Cabinet-level positions "demonstrated an aggravating hypocrisy." Romney, a Mormon, "wants America to be blind to his religious beliefs and judge him on merit," Ijaz wrote. "Yet he seems to accept excluding Muslims because of their religion, claiming they're too much of a minority for a post in high-level policymaking."

Ijaz urged Romney and other presidential candidates to "actively begin searching" for American Muslims and Arab Americans to serve in Cabinet posts to diminish the "risk (of) promulgating policies that once again put the U.S. straight in the sights of the terrorists who seek to bring America down."

The Council on American-Islamic Relations is calling on Romney to meet with Muslim leaders, pointing to press reports the Council sees as troubling.

Romney apparently made similar remarks before, saying at an earlier fund-raiser that he probably wouldn't appoint a Muslim to his cabinet, according to a report in the Talking Point Memo, based on the account of Irma Aguirre, a former finance director for the Nevada Republican Party and another witness.

And Ijaz told the Huffington Post that Romney's response to his article was misleading because his initial remarks weren't made in the context of combating Islamic extremism, but to possible cabinet appointments.

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Contributing: Hearst Newspapers