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

The American push in the Sadr City district is trying to weaken the militia grip in a key corner of Baghdad and disrupt rocket and mortar strikes on the US-protected Green Zone.

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

One rocket blasted the nearby city hall, while three hit parts of central Baghdad. An Iraqi police station was damaged by a rocket that failed to detonate, the US military said.

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

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

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

In the northern city of Mosul, one US soldier was killed in an attack by Sunni insurgents on an American patrol, the military said.