MANTIQA, Iraq -- Behind the wall of sandbags at the end of a narrow bridge in northern Iraq, a man in a black ski mask paces back and forth, brandishing a machine-gun and poking the barrel above the wall. Alongside him, a second militant in a red and white turban waves angrily. A third looks across the bridge with binoculars.

"If they shoot one bullet at us, we're going to return it with five," said Lt. Gen. Bapir Sheikhwasani of the Kurdish peshmerga militia as he tracked the Islamic State fighters through his own binoculars. "They are not the type of people who are up to stand against the peshmerga."

The Kurdish fighters, who number in the dozens, have been in a standoff with the extremists across the bridge for three months. They say U.S. airstrikes that began Aug. 8 have helped to weaken the Islamic State group in remote areas, but efforts to retake more populated areas have stalled because militants are taking refuge among civilians, making it harder for ground forces to go after them.

Stationed in an abandoned house they've barricaded in the town of Mantiqa, the Kurds are unable to effectively engage the militants, who retreat to the nearest town whenever they come under fire, the Kurdish fighters say.

Over the past 10 days, the peshmerga commanders have given strict instructions not to fire at the militants on the bridge. Sheikhwasani believes the Islamic State fighters may be plotting to blow up the bridge, but would need to lay explosives in the middle in order for the charge to be effective.

"They will not succeed if they try," Ahmed Hussein Abdullah, a peshmerga soldier on the bridge, said confidently.

The peshmerga on the Mullah Abdullah Bridge are quick to praise American forces, who recently expanded the air campaign to Syria in co-ordination with a coalition of Arab allies. Progress has been steady in Iraqi towns further west, where the peshmerga, backed by airstrikes, have managed to retake territory. But one-third of Iraq is still under the control of the Sunni militants.

Across the Mullah Abdullah Bridge, some 90 Islamic State fighters live among the residents, the peshmerga said -- most of them in hiding, afraid of bombardment from the air.

"Airstrikes very good," said one of the fighters in broken English, withholding his name because he's not supposed to speak to the media. "But we need more."

The unit in Mantiqa said it received a few new guns donated by several European countries to boost their offensive against the jihadi group, although they were unsure which country they came from. Sheikhwasani said that the weapons deliveries, while appreciated, are not nearly enough to guarantee their position on such a narrow front line.

Still, the fighters say they will hold their position on the bridge as long as they have to, and are prepared for the outcome, whatever it may be. "We said goodbye to our families," said Sheikhwasani, "not see you soon. We came here to defend our land and our families -- even if it means we never see them again."