The top commander of U.S. Marines in Iraq says the joint U.S. and Iraqi offensive in Fallujah has 'broken the back' of the insurgency in Iraq by taking away its safe haven.

Lieutenant General John Sattler told reporters today (Thursday) the 11-day operation has flushed the rebels from their hideouts, making it difficult for them to operate. He said Fallujah is not quite secure yet, and although humanitarian assistance has begun moving into the city, it is still too soon for residents to return.

Troops are present throughout Fallujah and are going building-to-building clearing weapons and explosives. General Sattler said a Marine and an Iraqi soldier were killed today when they came under fire during the clearing operations.

Their deaths bring to 51 the number of Americans killed along with eight Iraqi troops since the start of the offensive.

Meanwhile, gunmen have carried out bomb attacks in Baghdad and Kirkuk, killing four people. And in Mosul, four guards were wounded in a mortar attack on the governor's office.