SULTAN ABDULLAH HILLS, Iraq — Since retaking these barren hills in northern Iraq from the jihadists of the Islamic State, Kurdish pesh merga forces have dug in: excavating trenches, unfurling barbed wire and coordinating with the United States-led military coalition to identify targets for airstrikes.

The new outposts dotting the hilltops provide clear views of villages where Islamic State jihadists build truck bombs and launch attacks, but the Kurdish forces have no plans to advance, saying the territory is not theirs to fight for.

“Now our main job is defense,” said Maj. Gen. Mohammed Khoshawe, a field commander. “To defend the Kurds, this is the farthest we go.”

The ability of Kurdish forces in northern Iraq to retake and defend territory has been a rare success story for the Obama administration’s policy of coordinating with local ground forces to battle the Islamic State, also known as ISIS or ISIL. This week, the administration announced that it was considering expanding that effort with a network of new training bases in the Iraqi countryside.