WASHINGTON — Islamic State fighters are expected to make their last stand in a series of Euphrates River Valley towns and villages that American-backed Syrian and Iraqi forces are not expected to attack for months, American officials said Thursday.

Abu Bakr al-Baghdadi, the leader of the extremists’ self-styled caliphate, is believed to be hiding in the area, which stretches from Deir ez-Zor in Syria to Rawah in Iraq. So are the Islamic State cells that are responsible for planning attacks abroad, and were likely tied to Abdelbaki Essati, the shadowy imam who the authorities believe was at the center of the August terrorist attacks in Barcelona, Spain.

American military officials were quick to congratulate the Iraqi forces on their surprisingly swift victory in the northwest town of Tal Afar this week. But the seizure of that town is not seen by United States military commanders as an indication that the next phase of the campaign against the extremist fighters will be easy or quick.

Instead, the operation will need to deal with a complex array of political and military problems as American officials and their allies try to deliver the knockout blow against the militants. They must first ensure that American-backed fighters do not collide with converging Syrian government forces backed by Russia and Iran and Shiite militias supported by Tehran.