The U.S. will deploy one of its most advanced surveillance drones to the southern Philippines, joining other powers in escalating foreign involvement alongside the government’s beleaguered forces as a battle with Islamic State-linked militants grinds into a fourth month.

The Gray Eagle Unmanned Aircraft System, an upgraded version of the well-known Predator, will provide surveillance support to the Philippine military, the U.S. Embassy said in a statement Monday. The drone is capable of carrying cameras with infrared capability,...