Rockets or mortars pummeled the Green Zone on Monday even as U.S. troops battled to push Shiite insurgents beyond artillery range of the heart of Iraq's government. At least 38 suspected militants died in clashes in Baghdad's Shiite stronghold, the military said.

The fighting erupted Sunday afternoon amid a sandstorm that grounded U.S. helicopter gunships and unmanned drones that regularly patrol the sky over Sadr City.

The sprawling Shiite district of 2.5 million people is the main stronghold of the Mahdi Army of anti-American cleric Muqtada al-Sadr who is resisting government efforts to disarm the force.

He also has threatened to launch an "open war" against the U.S.-led foreign troops — a move that would jeopardize recent security gains.

The district, which is surrounded by walls along its outside perimeter with security checkpoints at all entrances, has been under siege since clashes erupted between the militiamen and U.S. and Iraqi forces on March 25.

The siege and daily combat in which hundreds have died since then have sparked worries that popular support for the government of Nouri al-Maliki could erode if he continues employing force to bring Sadrist militants under control.

On Monday, 30 Iraqi lawmakers from various political parties who had earlier visited Sadr City on a fact-finding mission, urged al-Maliki to end the confrontation saying innocent civilians and children were the main victims of the fighting.

"Yes, you can do it if you remember your own children," said a joint statement read by Mustafa al-Heeti, a Sunni member of parliament. "Your people (are) are demanding of you to intervene and solve the crisis peacefully."

Their appeal came after a day in which U.S. and Iraqi troops killed 38 suspected Shiite extremists in a series of firefights in which the Abrams tanks and Bradley armored personnel carriers fired on insurgents positions in Sadr City. Fifty-eight people, including five children and eight women, were injured in the clashes, local health officials said Monday.

The fighting erupted Sunday after militants unleashed a barrage of 107 mm rockets and 82 mm mortar shells at the Green Zone that houses diplomatic missions and the Iraqi government.

The near-daily shelling of the Green Zone has become acutely embarrassing for both Iraqi authorities and the U.S. military.

Iraq has been appealing to other Arab nations to open their embassies in Baghdad to lend international legitimacy to the regime. But their governments have responded by pointing to the bombardment as evidence that the Iraqi capital is just too unsafe for foreign diplomats.

Sadr City was constructed in the late 1950s to accommodate the inflow of Shiite migrants. It has grown since then but retained the neat, rectangular grid of streets originally set out by urban planners. U.S. officers say the insurgents now use that grid to align their fire when shelling the Green Zone, because the rows of parallel streets coincidentally point directly at the quarter.

Rather than mount an all-out assault, U.S. commanders have tried to limit the shelling by walling off the southern third of Sadr City. The wall, when constructed, will put the Green Zone out of range of light rockets and mortars.

Chinese-made 107 mm Katyushas have a range of five miles, while 82 mm mortars can exceed three miles. Much of the Green Zone lies at a distance of more than five miles from firing positions beyond the new wall.

The new wall will also allow security forces to better control the area by screening people coming through entry points in the barriers, and provide humanitarian assistance and basic services.

"It's a tried and true strategy that we'll continue to prosecute here because it has worked well in other locations, and we think it'll work well here," said Brig. Gen. Will Grimsley, an assistant division commander.

Col. John Hort, who commands U.S. troops on the southern edge of Sadr City, attributed Sunday's barrage to the thick dust kicked up by the storm which sharply degraded the performance of sensors and targeting lasers mounted on helicopters and unmanned drones.

He said 17 of the rounds that hit the Green Zone on Sunday were fired from inside Sadr City.

"Otherwise, we've had pretty good success in decreasing the attacks using Predator and Shadow (drones) and Apache helicopters over the past month," he said.

The shelling continued on Monday, with at least three explosions impacting in the government district. A parked car was damaged, but there were no reports of injuries.

In Sadr City, four policemen were wounded when Katyusha rockets slammed into a building housing Iraqi and U.S. forces in Sadr City, police said. A mortar attack targeting a U.S. military headquarters injured three civilians, they said.