updated 4/28/2008 4:15:41 PM ET 2008-04-28T20:15:41

Four American soldiers were killed Monday in rocket or mortar attacks in separate volleys in Baghdad.

The attacks raised the monthly U.S. death toll to at least 44, making it the deadliest since September.

Three of the Multi-National Division — Baghdad soldiers were killed just after 1 p.m. in an eastern section of the capital, the military said.

The statement did not give an exact location for the attack, but the area has been the scene of intense fighting recently between Shiite militiamen and U.S.-Iraqi troops.

Another soldier was killed by indirect fire in western Baghdad, the military said separately, using its term for a rocket or mortar attack.

In all, at least 4,056 members of the U.S. military have died since the Iraq war started in March 2003, according to an Associated Press count.

Militants shelled Baghdad's Green Zone on Monday as troops tried to push Shiite fighters farther from the U.S.-protected enclave and out of range for their rockets and mortars.

At least three more salvos hit the Green Zone in central Baghdad. In Sadr City — the stronghold of the Mahdi Army militia — U.S. soldiers battled deeper into the district a day after fierce clashes that killed at least 38 suspected militants, the military said.

U.S. soldiers killed seven more extremists Monday after coming under small-arms fire in Sadr City, the military said. Four of the suspects were killed in an airstrike and three others by an Abrams tank crew, according to a statement.

Sadr City has become the center of a showdown between the Iraqi government and the Mahdi Army, which is led by anti-American cleric Muqtada al-Sadr. U.S. forces have been increasingly drawn into the battles — including operations seeking to curb a rise in mortar and rocket attacks on the Green Zone.

Copyright 2008 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.

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