The exhausted Kurdish fighters leaned against a pair of antiquated green cannons on a hill overlooking this northern Iraqi village, the ground around them littered with shrapnel from fierce battles with Islamic State militants.

One of them, Moustafa Saleh, tapped the cannon with his mud-caked boots. “Russian-made,” he said, with a smirk. “My grandfather used the same one.”

Iraqi Kurdish fighters on the front lines of battle say they have yet to receive the heavy weapons and training pledged by the United States and almost a dozen other countries to help them push back the Sunni militants. […]