The attack comes a year to the day since the Islamic State jihadist group launched a sweeping offensive that overran much of Iraq's Sunni Arab heartland, and Baghdad is still struggling to push the militants back.
Sabah Abdullah, a member of the Amriyat al-Fallujah local council, said two militants wearing police uniforms mounted the attack during a council meeting.
They were killed before they could detonate their explosives but were still able to open fire.
There was no immediate claim of responsibility for the attack, but IS has carried out a string of similar attacks, including in Anbar province where Amriyat al-Fallujah is located.
IS has been driven out of some areas north and south of Baghdad but still holds much of western Iraq, including most of Anbar.
Baghdad's hopes of regaining ground in Anbar were dashed last month when IS overran provincial capital Ramadi, which Iraqi forces had defended for more than a year.