“At some point there is going to be a terrorist diaspora out of Syria like we’ve never seen before,” Mr. Comey said at a cybersecurity conference at Fordham University. “Not all of the Islamic State killers are going to die on the battlefield.”

Mr. Comey predicted that the military coalition would eventually succeed in crushing the Islamic State, but that “through the fingers of that crush are going to come hundreds of really dangerous people and they are going to flow primarily to Western Europe.” But some, he said, could well end up in the United States.

He drew a parallel between this scenario and the formation of Al Qaeda more than a quarter-century ago, which drew from fighters who had been radicalized fighting in Afghanistan in the 1980s and early 1990s.

“This is 10 times that or more,” Mr. Comey said. “This is an order of magnitude greater than anything we’ve seen before.”