The other option is for the United States to prioritize the removal of Mr. Assad, whose military has been responsible for far more carnage in Syria than the Islamic State. As long as Mr. Assad is in power, it will be difficult to get many Sunni rebels to help in the fight against the group.

“There is probably no solution to ISIS until there is a solution to Assad,” said J. M. Berger, a scholar at the Brookings Institution and a co-author of the book “ISIS: The State of Terror.” “That is the factor that paralyzes everything else.”

Emile Hokayem, a senior fellow at the International Institute for Strategic Studies, argued that Western powers needed to start identifying Mr. Assad’s government as part of the problem, because its brutality and sectarianism have allowed the Islamic State to thrive.

“Assad is not a sideshow,” he said. “He is at the center of this massive dilemma.”