The first bombing in Kirkuk was the deadliest of the attacks, killing eight people and wounding another eight, the officials said.
It was followed by a roadside explosion targeting the Kirkuk police chief's convoy and a car bomb that exploded nearby, killing two people and wounding nine between them.
In Tarmiyah, north of Baghdad, a suicide bomber on a motorcycle attacked a police checkpoint, killing one policeman and wounding four people, while a roadside bomb in the northern city of Mosul killed another policeman and wounded two.