The International Committee of the Red Cross (ICRC) said on Wednesday it had temporarily suspended humanitarian operations in Baghdad because the situation in the city was "chaotic and unpredictable".
The Geneva-based agency said a Canadian staff member had been missing since Tuesday afternoon and was feared seriously wounded but that it had not been able to search for him.
The ICRC said it feared that Vatche Arslanian, 48, had been wounded when a vehicle in which he was travelling with two other ICRC staffers came under fire. The other two escaped.
"Given the chaotic and totally unpredictable situation in the city, getting from one place to another involves incalculable risks," the ICRC said in a statement.
ICRC spokesman Roland Huguenin-Benjamin in Baghdad told CNN that ambulances had been unable to approach casualties in many parts of the city due to heavy crossfire as US troops battled sporadic Iraqi resistance.
"Casualties have been seen on the roads, on some bridges, and there was no possibility of evacuating them, for the reason that there was immediate fire as soon as anybody was trying to approach," he said.
"We are very, very concerned that a convoy of two clearly identified ICRC cars with large flags on were caught in such a situation. One of our colleagues who is a logistician of Canadian nationality...is feared seriously wounded and it has not been possible for hours to even approach the site."
He said the ICRC was "extremely distressed by the fact that there are numerous casualties that have been lying on roads where military engagements have been going on, and it has not been possible to remove them and to evacuate them to hospitals".
The delay in reaching casualties in Baghdad could prove fatal in many cases, Huguenin-Benjamin said.
"The problem is not the lack of medicine in the hospitals. The problem is the lack of respect for ambulances and respect for casualties, to give a chance for a minimum of security for people to be evacuated," he said.
The humanitarian agency was one of the few international organisations to keep international staff in Iraq during the conflict.
Jan Egeland, secretary general of the Norwegian Red Cross, told Reuters in Oslo that the ICRC convoy had been shot at while it was distributing relief supplies.
"Our colleagues in Baghdad have desperately sought to come to the rescue of their colleague but it has been impossible," he said.