On Sunday, the health ministry in northern Baghdad was hit by two mortar shells which slammed into the building, seriously injuring three civilians, Ahmad Muhammad Ali of the police said.
An al-Qaeda-linked group in Iraq also said on Sunday that it had executed 10 Shia Muslims from India and Pakistan, in an internet statement.
Six people, including four policemen, were killed in a car-bomb attack on a police patrol near the capital's main mortuary in the centre of the city.
Three civilian drivers were killed when insurgents began a combined attack of small-arms fire and a roadside bomb against an Iraqi army convoy near Abu Ghraib, an official said.
In another incident, a civilian was killed and 14 people wounded, when a car bomb blew up in central Baghdad's Karrada district, also directed at a police patrol.
One police vehicle was destroyed in the blast, which took place just across the street from a church.
In the Sunni neighbourhood of al-Adhamiya, a car bomb directed at an army patrol killed two soldiers and wounded two other people, including a soldier.
A suicide car bomber in the far northern city of Tal Afar rammed an Iraqi army observation post in the centre of town and detonated his vehicle, killing two soldiers and wounding two.
Five more were killed in the Diyala province.