A magnetic "sticky bomb" exploded against the car of Thanaa al-Massouli, a provincial councillor in the northern city of Mosul, killing her driver but leaving her unharmed, the officials said.
In a separate incident in the centre of Mosul, gunmen killed a policeman, while two roadside bombs left a policeman and a woman wounded in another attack in the city.
Two people were killed in the Bayaa area of Baghdad by gunmen who used guns with silencers, while another group of armed men killed a police officer in Fallujah, west of Baghdad, sources said.
A policeman who was travelling in the car with Obeidi was also killed.
With the latest attacks, 71 people have been killed in violence so far this month in Iraq, more than a third of them police officials, according to AFP figures based on security and medical sources.
Violence in Iraq has fallen from its peak at the height of the sectarian conflict in 2006 and 2007, but attacks remain common, and have killed more than 200 people in each of the first four months of this year.