BAGHDAD — A rocket slammed into Baghdad’s city hall and another hit a downtown park yesterday as more frightened civilians fled a Shiite militia stronghold where American-led forces are locked in fierce street battles.

The American push in the Sadr City district — launched after an Iraqi government crackdown on armed Shiite groups began in late March — is trying to weaken the militia grip in a key corner of Baghdad and disrupt rocket and mortar strikes on the American-protected Green Zone.

But fresh salvos of rockets from militants arced over the city, wounding at least 16 people and drawing American retaliation that escalated civilian panic and flight to safer areas.

One rocket — apparently aimed at the Green Zone — blasted the nearby city hall. Three 122 mm rockets hit parts of central Baghdad, including destroying some playground equipment in a park. An Iraqi police station was damaged by a rocket that failed to detonate, the U.S. military said.

American forcing used airstrikes and tank fire against suspected militia positions following a rocket attack late Monday in Sadr City, the military said. At least six people were killed.

An attack aircraft later fired two Hellfire missiles and killed three militants who were planting a roadside bomb in the Shiite neighborhood of New Baghdad on yesterday, the military added.

At least four civilians were killed in the clashes, hospital officials said.

The latest battles came as the Pentagon announced plans to cut American troop strength by about 3,500 toward its goal of withdrawing the bulk of its “surge” forces sent last year into Baghdad and surrounding areas.

More families, meanwhile, sought refuge in neighborhoods away from the fighting, which showed no sign of easing.

[Also yesterday, lawmakers said a new war spending bill proposed by House Democrats would prohibit using American aid to rebuild towns or equip security forces in Iraq unless Baghdad matches every dollar spent, the AP reported.]