Return to parliament of National Accordance Front could help national unity efforts.
US military commanders have been trying to expand their plan, first used in the violent western province of Anbar, of recruiting local Sunnis who are tired of al-Qaeda violence into special provincial police units.
Al-Qaeda is blamed for stoking sectarian hatred and violence between majority Shias and minority Sunni Arabs who were dominant under Saddam Hussein, the former Iraqi leader.
The US military began a security crackdown in Baghdad five months ago which initially helped bring down the number of sectarian murders but which also pushed al-Qaeda fighters out of the capital and into surrounding areas.
US and Iraqi forces later launched another big operation in the middle of June coinciding with the arrival of the last of 28,000 extra US troops in Iraq.