Shelling in Fallujah killed six and wounded 17 others, while a shooting targeting a local government offical killed two, AFP reported.
Friday's bloodshed comes only one day after more than a dozen bombings across the country which killed at least 23 and wonded many others. Violence in Iraq has increased to levels not seen since 2008.
Fighting in Fallujah began in late December when government forces cleared a Sunni-Arab anti-government protest camp. Anti-government forces then seized Fallujah and parts of Ramadi, with Iraqi security forces unable to take back the city.
According to the United Nations, more than 370,000 people have been displaced by the violence in Anbar province.