The bomber drove his car at a checkpoint in Siniya, west of the oil refining town, killing five national guards and two civilians, guard Captain Raad Jassim said on Friday.
Two other civilians were shot dead by guards nearby when they failed to stop at a checkpoint, hospital staff said.
Another national guard member was found shot dead near Falluja with a note on his body warning others against working with US forces.
The note attached to the bullet-riddled body read: "This is the fate awaiting anyone who collaborates with the occupier."
American forces are still fighting anti-US fighters in parts of Falluja.
Iraqi interim government officials say many fighters withdrew from the city before the recent massive US-led offensive and are still operating elsewhere.
Residents of the devastated city have slowly begun going home only to find the city in ruins.
Most who fled the fighting remain in refugee camps, exacerbating resentment of the US-led presence in the country.
Meanwhile, three loud explosions rattled central Baghdad late on Friday night, minutes after interim Iraqi Prime Minister Iyad Allawi delivered a speech on state television channels marking the end of the year.
It was not clear what caused the blasts, but fighters regularly mortar and rocket locations in Baghdad, particularly the Green Zone, home to the interim Iraqi government and the US embassy.
Further south, in the city of Amara, two British military vehicles were destroyed when an explosive device was detonated along a road they were travelling on.
Casualties among British soldiers have not been reported.