Witnesses said the attackers blew up two car bombs near the entrance of the compound in Baquba, the capital of Diyala province. Security officials said at least some of the attackers then entered the compound and opened fire.
There are reports of hostages, but the number is not clear. It is also not clear whether the situation has been resolved. There was no immediate claim of responsibility.
The attack came at a time when the provincial council is usually holding its weekly meeting. Police and security were deployed to the scene.
The attack raises concerns about the strength of Iraqi security forces as U.S. troops prepare to withdraw in just a few months.
The attack mirrored an incident in March, in which gunmen attacked Salaheddin governate offices in Tikrit, killing 58 people. Al-Qaida claimed responsibility for that attack.
Also, the U.S. reports two U.S. service members were killed Monday while conducting operations in southern Iraq. The Defense Department is investigating but has not released details.