BAGHDAD —  The U.S. military says rocket or mortar attacks against the U.S.-protected Green Zone and a military base elsewhere in Baghdad have killed three American service members and wounded 31.

A military official says two U.S. troops were killed and 17 wounded when rockets struck the Green Zone in central Baghdad. The official says another American service member died and 14 were wounded in another attack on a military base in the southeastern area of Rustamiyah.

The official spoke on condition of anonymity for lack of authorization to release the information.

Sunday's attacks come amid fierce clashes between Shiite militia fighters and U.S.-Iraqi forces.