A bomb placed on a bridge near the volatile city of Kirkuk exploded, wounding four people, the police there said.
Since the attacks, Falluja has become one of the most volatile cities in Iraq.
The military also said it conducted two airstrikes early and late on Saturday in the volatile city of Falluja to kill militants holding meetings.
Tamim Province, which includes the volatile city of Kirkuk, is almost certainly not one of those.
It also said a marine had been killed in western Iraq, possibly around the volatile city of Falluja, but gave no details.
The headquarters project, in the ethnically divided and volatile northern city of Mosul, is the second police-related contract to face harsh criticism recently.
But in this politically volatile city, suspicions cannot be quelled easily.
American military officials announced that two soldiers had been killed Monday in the volatile western city of Ramadi when a roadside bomb exploded on their patrol.
In the more volatile western city of Quetta, near the border with southern Afghanistan, unidentified gunmen shot and critically wounded a Pakistani general today.
In the volatile northern city of Mosul, at least seven more bodies were discovered Sunday.