Another 200 people were wounded in the blasts in Sadr City, in the east of the capital, in the attacks that came shortly after Iraqi political leaders said the new parliament will convene on Thursday, three days ahead of schedule.
In the latest attack, four police were wounded by the first car bomb in oil-rich Kirkuk, 250 kilometres north of Baghdad, police said.
The second car bomb killed two policemen as their patrol passed by around 15 minutes later.
The Sadr City explosions ripped through the poor neighbourhood at the peak shopping time, as residents bought food for their evening meal.
The district was quickly sealed off by Mehdi Army militiamen loyal to radical anti-American Shiite cleric Moqtada al-Sadr amid pandemonium.
The attack apparently bears the hallmarks of al-Qaeda in Iraq, a group that has said it wants to start a Shiite-Sunni civil conflict.
Saddam trial opens
Meanwhile, the trial of ousted Iraqi dictator Saddam Hussein and seven co-defendants charged with crimes against humanity has resumed, with more defendants testifying before the Iraqi High Tribunal.
Defendant Mohammed Azawi Ali, a former Baath party official from Dujail, took the stand.
On Sunday, three more local officials from the village testified, and along with Azawi Ali are present in court, with the defendants giving their testimony in turns.
Saddam and his co-defendants are accused of orchestrating a massacre of residents in the village of Dujail after the then-dictator escaped an assassination attempt there in 1982.