The U.S. military in Iraq says it is withdrawing 3,500 troops deployed there last year as part of a "surge" in U.S. forces.
The military says the U.S. troops will return to their base in the southern U.S. state of Georgia in the next few weeks.
U.S. and Iraqi soldiers have been fighting Shi'ite militants in Baghdad's Sadr City district in recent weeks as part of a crackdown on illegal militias. Iraqi officials say four people were killed in the latest battles in Sadr City late Monday and early Tuesday.
Elsewhere, the U.S. military says insurgents attacked a U.S. patrol in the northern city of Mosul Tuesday, killing one soldier and wounding another.
In another attack, the military says a car bomb exploded outside a building in the northern city of Tirkrit, killing three Iraqi civilians.
An Iraqi lawmaker, Hassan al-Rubaie, loyal to radical Shi'ite cleric Moqtada al-Sadr suspended his parliamentary seat Tuesday to protest the violence in Sadr City.
The U.S. military says U.S. and Iraqi forces have killed nine militants during operations in Baghdad since late Monday.
In other violence, the military says militants fired several rockets into central Baghdad early Tuesday, wounding seven people. The rockets hit a municipal building, a local park and an Iraqi police station.
In another development, Iraqi troops detained dozens of policemen suspected of helping Shi'ite militias in Baghdad late Monday.
Washington plans to complete the withdrawal of 30,000 troops from Iraq by July and then have a 45-day evaluation period before considering further pullouts.
Some information for this report was provided by AFP, AP and Reuters.