The heavily armed fighters peered out of a broken second-story window at their outpost in a crumbling house on the western edge of this shell-shocked city, where Islamic State is fighting a furious battle to hold on to the capital of its self-declared caliphate.

They ducked to avoid snipers camped in nearby high-rise apartments. Armed drones hovered nearby. Just before 2 p.m. came the crack of sniper fire.



For the record: An earlier version of this article said slain U.S. volunteer Nicholas Warden, 29, was from Buffalo, N.H. He was from Buffalo, N.Y.

“That’s our guy,” Kevin Howard, 28, said as he rose and prepared to return fire.