From Ajami's obit in the Times (my emphasis):
An Arab, Mr. Ajami despaired of autocratic Arab governments finding their own way to democracy, and believed that the United States must confront what he called a “culture of terrorism” after the 2001 terrorist attacks on New York and Washington.
Condoleezza Rice summoned him to the Bush White House when she was national security adviser, and he advised Paul Wolfowitz, then the deputy secretary of defense. In a speech in 2002, Vice President Dick Cheney invoked Mr. Ajami as predicting that Iraqis would greet liberation by the American military with joy.
In the years following the Iraqi invasion, Mr. Ajami continued to support the action as stabilizing.