The International Committee of the Red Cross (ICRC) says two key Baghdad hospitals, and many other smaller ones, have been ransacked, as looting spreads across the capital.
The al-Kindi hospital has been receiving Baghdad's injured
ICRC spokeswoman Nada Doumani told BBC News Online that armed looters had stripped the al-Kindi, a key hospital in north-eastern Baghdad, of everything, including beds, electrical fittings and medical equipment.
She said another major hospital, the 650-bed Medical City, was also surrounded by armed men and was running low of water and medical supplies.
Baghdad's hospitals have already been under severe strain in recent days as they try to cope with the casualties caused by the coalition's aerial bombardments of the capital, as well as fighting on the ground.
Many smaller hospitals in the city, which is now mostly under the control of US troops, have closed for fear of being looted.
United Nations Secretary General Kofi Annan and Britain's International Development Secretary, Clare Short, both said law and order in Baghdad is now a major concern.
The Red Cross spokeswoman said organisation staff had on Thursday been unable to get to both the al-Kindi and the Medical City hospitals because of armed people in the streets.
"Al-Kindi has been looted by an armed group. Security in the city is very bad and people are not daring to go to the hospitals.
"We have heard that smaller hospitals are closed because people are too scared to open them to have them looted by armed men," said the spokeswoman.
"If we cannot get to the hospitals because of the situation it means that normal citizens cannot get there either."
The ICRC suspended operations in Baghdad on Wednesday after a Canadian member of the humanitarian team was killed in the capital.
Vatche Arslanian, 48, was travelling in a Red Cross vehicle when it was hit by gunfire on Tuesday.
The agency's work was halted because it said staff movement involved "incalculable risks".
On Thursday, the ICRC team tried to re-start work, but armed men on the streets have hindered their efforts to get to the city's hospitals.
If we cannot get to the hospitals because of the situation it means that normal citizens cannot get there either
Nada Doumani, ICRC spokeswoman
Law and order broke down on the streets of Baghdad following the push by US troops into the centre of the Iraqi capital on Wednesday.
Looters took food, furniture, ornaments, carpets and other items from government offices, shops, homes and Saddam's Hussein's palaces.
The Red Cross spokeswoman repeated an earlier plea by the organisation for US forces to restore law and order on the streets of Baghdad.
She said: "It is the responsibility of the forces in the city to ensure the safety of essential services, such as hospitals."
Speaking as he arrived at UN headquarters on Thursday, Mr Annan said after scenes of looting "obviously law and order must be a major concern".
Ms Short said British and American troops were required, under the Geneva Convention, to provide humanitarian assistance to civilians, to maintain order, and to keep the civil administration running.