Seven civilians, three soldiers and four militants were killed in the violence in the town of Hawijah, west of Kirkuk, army Staff Major General Mohammed Khalaf al-Dulaimi said.
One suicide bomber detonated an explosives-rigged vehicle near a police station while a second blew up another near a local administrative building.
Militants then targeted those structures and a local council building with mortar fire, and gunmen attacked, leading to clashes with soldiers.
Soldiers were searching for the remaining militants, who left the area, Dulaimi said.
Death tolls in Iraq have reached a level not seen since 2008, when the country was just emerging from a brutal sectarian conflict.