“It bugs the hell out of me,” said Sgt. George Lewis, Captain Veath’s platoon sergeant in Company B, Third Platoon, First Battalion, 14th Infantry Regiment. “We don’t see any progress being made at all. We hear these guys in firefights. We know if we are not up there helping these guys out we are making very little progress.”

Image Iraqi soldiers on Tuesday after abandoning their posts on a joint mission with American troops in the Sadr City area of Baghdad. Credit... Joao Silva for The New York Times

Company B moved into Sadr City at the end of March as part of a broader effort to secure the southernmost portion of the densely populated Sadr City.

That area has been used by militias to fire 107-millimeter rockets toward the Green Zone. The Americans’ mission is to stop the rocket firings and help the Iraqi government establish a modicum of control.

Some Iraqi soldiers have fought hard. American soldiers have been regularly coaching them on how to protect their patrol bases, conserve ammunition and evacuate their wounded.

One big problem is that the Iraqi troops have responded to militia gunfire with such intense fusillades that the soldiers have endangered civilians, American soldiers and even their own forces. The barrage of Iraqi Army fire has become such a regular occurrence that some American soldiers are worried that militia fighters have tried to insert themselves between nearby Iraqi units to induce the Iraqi soldiers to fire on one another.

In a recent visit to the Iraqi forward position, First Sgt. Martin Angulo of Company B sought to coach the Iraqis on how to use their newly acquired M-16s to direct precision fire at a militia sniper who had been tormenting the Iraqi forces from an alleyway.

The problem on Tuesday, however, was more serious: an Iraqi retreat that left a gaping hole in the most forward position on a critical thoroughfare in the Tharwa section of Sadr City.