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ISNA promotes itself as a voice of moderation that seeks Muslim-Jewish reconciliation and campaigns against what it calls “Islamophobia.”

The publication Jewish Week, in an April 2 article, quoted a rabbi as praising ISNA for reaching out to the Jewish community in the United States. “They feel strongly it is time to move forward,” the rabbi said.

Some counterterrorism specialists criticize ISNA for failing to condemn terrorist attacks on Israel.

Steven Emerson, who directs the Investigative Project on Terrorism, recently wrote that the silence of ISNA and other Muslim groups after Hamas killed eight Israeli students “shows their unwillingness to condemn the terrorist act and its glorification.”

Michael Ledeen, a terrorism analyst at the American Enterprise Institute for Public Policy Research, backed Mr. McCain’s definition of the enemy.

“Islamic terrorism is purely descriptive,” he said. “It doesn’t group the enemy under the Islamic brush stroke because there are plenty of terrorists and extremists who are not Islamic. So it’s just a way of specifying who they are.”

Of ISNA’s criticism, Mr. Ledeen said, “They’re just silly. What a silly thing to say. I talk of Marxist extremists and nationalist extremists. They just don’t want people to say there are Islamic terrorists, which there are. Too bad.”