In Baghdad, three civilian drivers were killed when insurgents launched an attack on an Iraqi army convoy near Abu Ghraib.
Meanwhile a civilian was killed and 14 others wounded, including four policemen, when a car bomb blew up in central Baghdad's Karrada district, targeting a police patrol.
The attacks come a day after 31 people, mostly women and children, were killed in a bomb blast in Baghdad's Shi'ite district of Sadr City, the day Sunnis began the fasting month of Ramadan.
More than 30 people were also wounded in the daylight blast that ripped through the area while families were lining up to collect kerosene used for cooking fuel.
Iraqi Prime Minister Nouri al-Maliki has pleaded for Shi’ites and Sunnis to put aside their differences and end sectarian violence during Ramadan.
But a disagreement over the day Ramadan begins has served emphasise just how deep the differences are between the country's two major Muslim sects.
Sunni Arabs began observing Ramadan on Saturday, while Iraq's most influential Shi’ite cleric Grand Ayatollah Ali al-Sistani declared the start of Ramadan on Monday.