The US-led offensive in Falluja has "broken the back of the insurgency" across Iraq, a senior US marine commander has said.
The assault on Falluja is aimed at stabilising the country
Lt Gen John Sattler told reporters the operation had flushed the rebels out of their safe haven and scattered them.
But he said remaining insurgents were still a problem as US forces moved through the Iraqi city.
Iraq's interim government is planning to send food and medical teams to civilians in Falluja.
Gen Sattler, commander of the force leading the Falluja operation, had no information about civilian deaths.
Fifty-one US soldiers and eight Iraqi soldiers have been killed since the assault began on 8 November, Gen Sattler said.
He said media estimates of 1,200 insurgents killed was "probably a safe number".
'Breathe down their neck'
The BBC's Pentagon correspondent Nick Childs says Gen Sattler appeared to go further than other top US generals and defence officials to date.
"This is going to make it very hard for them [insurgents] to operate," Gen Sattler said in a briefing outside Falluja, relayed to Washington via a video link.
"I'm hoping that we'll continue to breathe down their neck, quick-turn this tactical intelligence, find them in areas... that they're not familiar with, where they will in fact be easier to capture or bring to justice," he added.
US marines are bombing Falluja insurgents from the air
However, marine intelligence officials have warned that the insurgency would rebuild if the US military did not maintain a large presence in Falluja.
The US-led assault on the Sunni Muslim city, 50km (30 miles) west of the capital Baghdad, is aimed at stabilising the country before planned elections in January.
Correspondents say the next few weeks will show whether the stick of superior US firepower and the carrot of elections can diminish the insurgency.
Iraqi and US authorities, who have regained control of most of Falluja, have been playing down warnings by the Red Cross of a humanitarian crisis in Falluja.
But on Thursday, a spokesman for the interim Iraqi government said health services would be restored, and housing and reconstruction needs assessed.
Residents who had fled would be helped to return, and each family would receive $100 compensation, the spokesman said.
Most of the city's residents fled before the assault began but tens of thousands of civilians could still be hiding in their homes.
The International Committee of the Red Cross (ICRC) says the city is without running water or electricity, and wounded people are unable to reach medical care because of the fighting.
It has called for an independent assessment of the situation facing those still living in Falluja.
The ICRC is negotiating with US forces to open a "humanitarian corridor" into the city, an agency spokesman said.
US-led forces have been continuing to encounter fierce displays of resistance in southern areas of Falluja.
The US is carrying out aerial bombing raids on houses where rebel fighters are believed to be taking shelter.
Meanwhile, a mutilated woman's body found in Falluja on Sunday has been flown out of Iraq for DNA tests to see if it is that of kidnapped aid worker Margaret Hassan.