The International Red Cross has urged US forces to restore the Iraqi capital's power supply and other basic services as the threat to public health grows daily.
US forces face anger on the streets
Roland Huguenin-Benjamin of the
International Committee of the Red Cross (ICRC) told the BBC that less than half of the city's hospitals were functioning - the rest had been ransacked by looters.
"There has to be a civil administration, it should be empowered and start working, the sooner the better," he said.
Despite the general breakdown of law and order there have been some successes in the hunt for regime fugitives - the latest being the arrest of the former finance minister, Hikmat Ibrahim al-Azzawi.
Iraqi police captured him in Baghdad and handed him over to US marines on Saturday.
CAPTURED IRAQI LEADERS (AS RANKED BY US FORCES)
24. Samir al-Aziz al-Najem
45. Hikmat Ibrahim al-Azzawi
51. Watban Ibrahim al-Tikriti
52. Barzan Ibrahim al-Tikriti
55. General Amir al-Saadi (surrendered)
A Central Command spokesman, Captain Stewart Upton, said Mr al-Azzawi "could have information on the locations of money that belongs to the Iraqi people".
He is number 45 on the coalition's list of 55 most wanted Iraqi officials, and the eight of diamonds in the US forces' pack of cards featuring them.
Two more suspects have surrendered to US forces.
US officials named them as Imad Hussein Abdallah al-Ani, said to have been involved in Iraq's suspected nerve gas programme, and Khala Khadr al-Salahat, an "international terrorist" belonging to the Palestinian Abu Nidal organisation.
US marines involved in seizing Baghdad have now withdrawn from the city, handing over to regular US Army troops, who are said to be more familiar with peacekeeping and reconstruction duties.
But, in a further sign of chaos, looters can now be seen selling stolen weapons and ammunition - including Kalashnikov assault rifles - openly on the streets.
Correspondents say much of Baghdad still has no running water.
MIDDLE EAST AFTER SADDAM
The after-effects of the war for the region
The lack of sewage treatment and garbage collection is posing health problems, Mr Huguenin-Benjamin warned.
"One of the major sewage treatment plants in the city was damaged in the war, then looted. It is in urgent need of maintenance and repair - otherwise there is a very serious health hazard if sewage is not treated properly in the hot summer."
Despite the general chaos, doctors are returning to hospitals and working without pay, he said.
But the lack of electricity means that medicines cannot be refrigerated and much hospital equipment lies idle, he said.
The UN children's fund Unicef says piles of rubbish are accumulating at the hospitals and up to 70% of patients at the children's hospital now have diarrhoea.
Meanwhile, reports say the first major convoy of food aid has arrived in Baghdad from Jordan. The flour and other goods will be stored in warehouses until distribution can be arranged.
The BBC's Caroline Hawley in Baghdad says Iraqis remain deeply suspicious of American motives, noting that the oil ministry is one of the few government buildings not to have been looted.
Mass demonstrations against the US presence are a daily occurrence, she says.
A prominent Iraqi exile, former Foreign Minister Adnan Pachachi, has spoken out against the US Government awarding big reconstruction contracts for Iraq.
"No one has the right to commit Iraq to obligations and costs. Only an Iraqi government can do that," he said in Kuwait.
Foreign ministers of the six states which border Iraq, plus Egypt and Bahrain, have called for US-led forces to pull out of Iraq as soon as possible.