The deadliest attack took place in Baghdad's Bab al-Sharji area, where a bomb went off outside a small restaurant, killing seven civilians and wounding 22, a police officer said. Another bombing in the central Sibaa area killed three civilians and wounded 11, he said.
A health official confirmed the casualty figures. Both officials spoke on condition of anonymity as they were not authorised to release the information.
No group immediately claimed responsibility for the bombings. Iraq sees near-daily attacks, mainly targeting the country's Shiite majority and security forces. The attacks often are claimed by the Islamic State group, which seized about a third of the country last year.
The officials, who spoke only on condition of anonymity as they were not authorised to talk to journalists, said the government forces had recaptured seven villages and that security forces and Shiite fighters suffered causalities, without elaborating.
The Islamic State group's offensive has become Iraq's worst crisis since the 2011 withdrawal of US troops. It has exploited widespread Sunni discontent with the Shiite-led government in Baghdad.