Police say the bigger explosion happened when a bomb hidden in a pickup truck hauling vegetables tore through a market in Samarrah, 95 kilometers north of Baghdad. Police say that blast killed 18 and wounded 32.
Police say another car bomb went off in Abu Ghraib, on the western outskirts of Baghdad. They say it killed five and wounded eight.
Hospital officials confirmed the casualty figures. All officials spoke on condition of anonymity because they weren't authorised to release the information.
More than 4,000 people have been killed in attacks in Iraq since April, when the pace of killing accelerated to levels unseen since 2008.