Akram Mahmud Najm, a member of a local council, was killed on Monday and another councilor was wounded in the northern city of Mosul. The gunmen fled after firing on the car, police said.
Also on Monday, armed fighters fired mortars at a Baghdad police station wounding two policemen and three civilians. The attacks on Monday coincided with a signing ceremony for Iraq's interim constitution.
A projectile also hit a nearby house, smashing windows and blowing a hole in a wall, but causing no casualties, witnesses said. Another loud blast after the signing ceremony was a controlled explosion by the US military, the Army said.
Security forces have been on high alert for possible attacks, aimed at disrupting the signing ceremony.
On Sunday, fighters fired rockets at the "Green Zone" in Baghdad, the headquarters of the US-led administration in Iraq. The US military said there were no serious injuries.