BAGHDAD — Barack Obama’s speech in Cairo last Thursday was “soft spoken and eloquent,” said Moqtada al-Sadr, the radical Iraqi cleric, grudgingly, since he also said he despised it. It was a speech that meant different things to different people, a quality that has been much noted in this president. He supported Israel, but reached out to the Muslim world in an unprecedented way. Some friends were troubled, others reassured. Some of America’s enemies denounced it, but none dismissed it. Not even the arch-enemies at whom, in some important way, the speech was directed.

Just the day before, in fact, a pre-emptive audio tape attributed to Osama bin Laden warned his followers not to trust whatever Mr. Obama would say. And as it turned out, his fear was justified. In the view of Fawaz Gerges, the president’s speech was above all else about the war on terror, a direct attack on Mr. bin Laden and the mindset he promulgates.

“Barack Obama is not just trying to reach out to Muslims for the sake of it,” says Mr. Gerges, a professor of Middle Eastern studies at Sarah Lawrence College and an authority on modern jihad. “He’s trying to hammer a deadly nail in Osama bin Laden’s message.” What President Obama understood more than his predecessors, Mr. Gerges says, is that it is not a war that can be won militarily, but only ideologically.

Jarret Brachman, a former West Point terrorism expert and author of a recent book, “Global Jihadism,” said the speech “was the most important strategic step we’ve taken in this war.”