US commanders say more attacks are taking place outside Baghdad because of a nearly seven-week-old crackdown in the capital.
Child casualties
Police said the attacker in Kirkuk on Monday targeted the police criminal investigation department.
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Brigadier General Sarhat Qadir, a local police spokesman, said the bomber rammed his vehicle into the concrete blast barriers surrounding the police station and detonated the explosives, hidden under a load of flour.
One woman, holding her screaming daughter and son, said: "I was preparing lunch for my children when the explosion happened. I thought the house was going to collapse."
Qadir told the Associated Press that 13 people were killed, seven houses destroyed and 35 cars set ablaze by the blast. He said the toll was expected to rise.
He also said 137 were wounded and that at least 20 children who had been playing outside at a nearby school were among the casualties but could not provide a breakdown.
Another police official, Brigadier Torhan Abdul-Rahman, told Reuters that six people were killed and more than 100 people wounded.
Attackers have increasingly used truck bombs in recent months.
A truck bomb in the northern town of Tal Afar last Tuesday killed 152 people, making it the deadliest single attack of the four-year-old war.
Baghdad bombing
Also on Monday, a car parked in a garage exploded in Baghdad, killing at least three people and wounding 10, police said.
The blast took place about 10am (07:00 GMT) near a government property registration agency in the Bayaa neighbourhood, an area with a mixed population of Sunnis and Shias in western Baghdad.
Police said five cars and nearby buildings were damaged.