Humanitarian officials are increasingly concerned about civilians still trapped inside Fallujah as well as thousands of refugees who fled their homes in advance of the US decision to take the city by force.
They said that residents who were too old, sick or poor to leave the city had been left without access to food, water, electricity or medical treatment and that the situation was particularly precarious for children.
In a statement, Louise Arbour, the UN high commissioner for human rights, said: "There have been a number of reports during the confrontation alleging violations of the rules of war designed to protect civilians and combatants. Those responsible for breaches - including deliberate targeting of civilians, indiscriminate and disproportionate attacks, the killing of injured persons and the use of human shields - must be brought to justice."
She added: "[I am] particularly worried over poor access by civilians still in the city to the delivery of humanitarian aid and about the lack of information regarding the number of civilian casualties."
The number of civilians killed during the eight-day battle for the city remains unclear. One report yesterday quoted an unnamed Red Cross official in Baghdad as saying up to 800 civilians were feared dead.
In Geneva Anatonella Notari, the chief spokeswoman for the International Committee of the Red Cross (ICRC), said that the agency had been unable to make an independent examination of most of the city. Officials from its sister organisation, the Red Crescent, had spent three days in areas controlled by US and Iraqi troops, but had been prevented from crossing the Euphrates river into the centre of Fallujah. The Red Crescent aid convoy returned to Baghdad on Monday after being refused access by the US military, who cited security concerns.
"It is very difficult [to make accurate estimates] because the information we're getting is only partial," she said.
Ms Notari said there was a problem with the thousands of civilians living in tent cities around Fallujah. She said that in recent days the ICRC had helped an estimated 40,000 people at three locations close to Fallujah. She said it was known that at least 5,000 people had left for Baghdad before the battle for the city commenced.
A report from the Inter Press Service quoted an unnamed official with the Red Cross who estimated that while 800 civilians had been killed, up to 50,000 civilians had remained in the city. Most estimates have put the figure much lower than this but there is no way of accurately telling how many may remain.
"Several Red Cross workers have returned from Fallujah as the Americans won't let them into the city," said the official. "They said the people they are tending to in the refugee camps outside the city are telling horrible stories of suffering and death inside Fallujah."
Reporters inside the city have described streets strewn with charred bodies. In line with Muslim burial rites, Iraqis yesterday continued collecting bodies for burial, finding 14 in total.
"We're Iraqis and they're Iraqis and we want to get them," Mohammed Ali, a 32-year-old farmer helping to remove bodies, told an journalist in the shattered city. "It's in our religion. The rules say that relatives or families or Arabs should help them."
The US military has said that 38 Americans, six Iraqi soldiers and an estimated 1,200 insurgents were killed in the offensive.
"This exemplifies the horrors of war," said US Marine Capt PJ Batty of the body pick-up. "We don't wish this upon anyone, but everyone needs to understand there are consequences for not following the Iraqi government."