But to Mr. Gingrich, whose campaign did not respond to a request for comment, the administration’s language smacks of the willful blindness of an earlier era. “The left’s refusal to tell the truth about the Islamist threat is a natural parallel to the 70-year pattern of left-wing intellectuals refusing to tell the truth about communism and the Soviet Union,” Mr. Gingrich said.

Shariah (literally, “the path to the watering place”) is a central concept in Islam. It is God’s law, as derived from the Koran and the example of the Prophet Muhammad, and has far wider application than secular law. It is popularly associated with its most extreme application in societies like Afghanistan under the Taliban , including chopping off a hand as punishment for thievery.

But it has always been subject to interpretation by religious authorities, so its application has varied over time and geography, said Bernard G. Weiss, professor emeritus at the University of Utah and an authority on Islamic law.

“In the hands of terrorists, Shariah can be developed into a highly threatening, militant notion,” Professor Weiss said. “In the hands of a contemporary Muslim thinker writing in the journal Religion and Law, Shariah becomes an essentially pacifist notion.”

The Arab Spring has set off a lively political and scholarly debate over the growing power of Islamists in Egypt , Tunisia and Libya . But those are all overwhelmingly Muslim countries. The idea that Shariah poses a danger in the United States, where the census pegs Muslims as less than 1 percent of the population, strikes many scholars as quixotic.

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Even within that 1 percent, most American Muslims have no enthusiasm for replacing federal and state law with Shariah, as some conservatives fear, let alone adopting such ancient prescriptions as stoning for adulterers, said Akbar Ahmed, chairman of Islamic studies at American University in Washington, who spent a year traveling the United States and interviewing Muslims for his 2010 book “Journey into America: The Challenge of Islam.”

The notion of a threat from Shariah to the United States “takes your breath away, it’s so absurd,” Dr. Ahmed said. He sees political demagoguery in the anti-Shariah campaign, which fueled rallies against mosques in the last two years from Manhattan to Tennessee .

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All of the Republican presidential candidates have been asked about the supposed threat from Shariah. Representative Michele Bachmann told the conservative Family Research Council in a November speech that Shariah “must be resisted across the United States,” endorsing moves by several states to prohibit judges from considering Shariah.

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Mitt Romney said in a June debate: “We’re not going to have Shariah law applied in U.S. courts. That’s never going to happen.” He immediately added, “People of all faiths are welcome in this country.”

For Mr. Gingrich, concern about Shariah has been a far more prominent theme. He and his wife, Callista, produced and narrated a 2010 film on the threat from radical Islam, “America at Risk,” that discusses the danger of both terrorism and Shariah against a lurid background of terrorist bombings, bloody victims, wailing sirens and chanting Muslim crowds. (Mrs. Gingrich does say, at one point, “This is not a battle with the majority of Muslims, who are peaceful.”)

One Muslim activist who is shown in the film calling for “separation of mosque and state,” Dr. M. Zuhdi Jasser, said he appreciated Mr. Gingrich’s support in an ideological contest with large Muslim advocacy groups in the United States that he believes have an Islamist slant.

But Dr. Jasser, a Phoenix physician and founder of the American Islamic Forum for Democracy, said non-Muslims like Mr. Gingrich were not the most effective advocates for what he believes is really a debate within Islam.

“Unfortunately, as long as a non-Muslim opens the discussion, whether it’s Gingrich or someone else, it’s going to hit a brick wall in the Muslim community,” Dr. Jasser said.

Mohamed Elibiary, a Muslim and an adviser to law enforcement agencies in Texas and to the Department of Homeland Security , is a conservative Republican who said he once idolized Mr. Gingrich. He said he no longer did.

He said the anti-Shariah campaign in the United States was “propaganda for jihadists,” offering fuel for the idea of a titanic clash of faiths. Those who truly want to protect American values should talk to Muslims, he said, not demonize them.

“There are plenty of American Muslim patriots who will defend American freedoms,” Mr. Elibiary said. “But you can’t be anti-Islam and find those allies.”