“If there is anything ISIL has learned from its previous iterations as Al Qaeda in Iraq, it is that they need succession plans because losing leaders to counterterrorism operations is to be expected,” said one intelligence official, using an alternative name for the group. “Their command and control is quite flexible as a result.”

American officials caution that intelligence experts are still assessing ISIS’s current strength and that pinning down the precise number of its fighters is difficult, in part because it is not easy to identify who is a core member of the group and who might be sympathizers fighting alongside them.

Estimates of the number of fighters that might be affiliated with ISIS vary from more than 10,000 to as many as 17,000. That includes an initial vanguard of about 3,000 who swept into Mosul from Syria in early June and ISIS reinforcements from Syria since that time, as well as thousands of new foreign recruits and thousands of Iraqi Sunnis, like Baathists, who at least for now are allied with ISIS.

So far, the military strategy that the Obama administration has employed to confront ISIS has been limited in scope. Since Aug. 8, the United States has carried out 90 airstrikes to halt the militant group’s advance to Erbil, to help Kurdish and Iraqi government forces retake the Mosul Dam and to protect Yazidi civilians trying to escape from Mount Sinjar.

While American air power appears to have been relatively successful in those limited missions, some military officials say that the only way to deal a major setback to such a mobile adversary is to attack ISIS fighters throughout the battlefield.