Iraqi army captain Mohammed Fayad from Fallujah said four soldiers were killed and three wounded when a missile hit their camp northeast of the town.
Police captain Ahmad Faisal said three soldiers were killed in clashes with unknown gunmen in the centre of the town.
A bullet-riddled corpse was also found in Fallujah, in mainly Sunni Al-Anbar province.
Iraq's Anbar province continues to be a battlefield for security forces, especially US troops. The bulk of US military losses in Iraq have been in the province located west of Baghdad.
Iraqi take over
It comes as Iraq took control of security from Italian and Romanian troops in the largely Shiite southern province of Dhi Qar, paving the way for the coalition forces to head home.
The relatively peaceful province is the second of the violence-ravaged country's 18 provinces to be handed over to Iraqi forces by the US-led coalition after the July transfer of power in Al-Muthanna province.
Prior to Thursday's handover, 1,860 Italian and 430 Romanian troops were in charge of security in Dhi Qar, of which Nasiriyah is the capital.
"Today we received the security file for the province of Dhi Qar which follows the handover of Al-Muthanna," Prime Minister Nuri al-Maliki said during a handover ceremony.
"We will continue to receive control of other provinces as we manage to get our country back from the hands of the Baath dictatorship," he said in a reference to the former regime of ousted Iraqi leader Saddam Hussein.
Mr Maliki said stiff "challenges" still lay ahead.