WASHINGTON—The Trump administration has asked at least 21 of its allies to provide troops and other logistical support in Syria to prevent an Islamic State resurgence, but nearly half so far have declined and others have agreed to provide only nominal support, U.S. and foreign officials said.

The hurdles to assembling an allied force in Syria have complicated U.S. planning and troop withdrawal efforts in the period following the capture last month of the last Islamic State-held territory in Syria, officials said.

Besides...