BAGHDAD — Suspected Shiite militants lobbed rockets and mortar shells into the American-protected Green Zone and a military base elsewhere in Baghdad yesterday, killing three American troops and wounding 31, officials said.

The attacks occurred as America and Iraqi forces battled Shiite militants in Sadr City in some of the fiercest fighting since the radical cleric Moqtada al-Sadr ordered a cease-fire a week ago. At least 16 Iraqi civilians were killed and nearly 100 wounded in the fighting, according to hospital officials. A military official said two American troops died and 17 were wounded in the attack on the Green Zone, which houses the American Embassy and the Iraqi government headquarters in central Baghdad.

Another American service member was killed and 14 were wounded in the attack on a base in the southeastern Baghdad area of Rustamiyah, the official said, speaking on condition of anonymity because he wasn’t authorized to release the information.

The U.S. military said separately that an American soldier was killed yesterday in a roadside bombing in the Diyala province north of Baghdad. An American soldier assigned to the division operating south of the capital also died yesterday from non-combat related injuries, according to a statement. The deaths raised to at least 4,018 members of the U.S. military who have died since the Iraq war started in March 2003, according to an Associated Press count.

A senior U.S. military official, also declining to be identified for the same reason, said the rockets were fired at the Green Zone from Sadr City, while the mortar shells came from another predominantly Shiite neighborhood in eastern Baghdad, New Baghdad. American commanders have blamed what they call Iranian-backed rogue militia groups for launching missiles against American forces. The strikes occurred despite a push by the U.S. military to prevent militants from using suspected launching sites on the southern edge of Sadr City, the Baghdad stronghold of the Mahdi Army of Mr. Sadr.