Sewage and rabid animals pose a significant health threat in Falluja, US military officials have warned.
US marines have been ordered to thin out Falluja's animal population
An army spokesman said the estimated 250,000 people that fled the assault cannot return until the risk posed by stray animals and sewage is eliminated.
US forces retook the insurgent bastion amid heavy fighting last month.
The Red Cross is waiting for US forces to give it the go-ahead to restore the city's water supply and help identify the hundreds of gathered corpses.
'Warehouse of bodies'
"Many streets are flooded with sewage water," Red Cross spokesman Ahmad Rawi, who has just returned from Falluja, told the BBC News website.
He said the city's water treatment plant has to itself be drained before an assessment can be made of how badly it has been damaged.
Another priority for the agency, Mr Rawi said, is the identification of "hundreds of bodies" collected and stored by US-led forces in a former potato warehouse.
Photographs of the corpses have to be taken and circulated among refugees from the city so that they could be identified and buried as soon as possible.
The Red Cross could not confirm whether the warehouse had refrigeration facilities to prevent the bodies from decaying.
As well as water-borne diseases, US forces say dogs that have fed on corpses pose a risk to returning refugees.
US soldiers have been killing the stray animals to prevent the spread of rabies, the BBC's Caroline Hawley reports.
Marines interviewed by AFP news agency said orders had been given to "thin out" the city's animal population.
Rabies is spread by the saliva of infected animals, who often behave aggressively because of the disease.
Once transmitted to humans, it is usually fatal.
The US military has not said when it will allow refugees back into Falluja.
Officers are planning to use iris scans and fingerprints to screen males of a fighting age who try to re-enter the city, our correspondent reports.