Those responsible for any violations – US-led forces, Iraqi government troops or fighters - should be brought to justice, the former UN war crimes prosecutor said in a statement on Tuesday.
"There have been a number of reports during the current confrontation alleging violations of the rules of war designed to protect civilians and combatants," Arbour said.
She gave no specific examples. But on Monday, Amnesty International accused both sides of breaking rules designed to protect civilians and wounded combatants during conflict.
Attacking US and Iraqi troops had failed to take necessary steps to ensure non-combatants did not come under fire. Resistance fighters had abused flags of truce and fired indiscriminately, the London-based group said.
Amnesty: US-led forces failed to
ensure non-combatants' safety
All violations of international humanitarian and human rights law must be investigated, including "the deliberate targeting of civilians, indiscriminate and disproportionate attacks, the killing of injured persons and the use of human shields", Arbour said.
Controversy over the Falluja offensive has been fuelled by video footage showing a US marine shooting dead a wounded and unarmed Iraqi in a mosque in Falluja on Saturday.
The US military has begun an investigation into possible war crimes over the incident, filmed in a television pool report by NBC.
Arbour, the UN High Commissioner for Human Rights, said she was especially worried about civilians still in Falluja, who might lack access to aid, and about the paucity of information on civilian casualties.
Iraq's interim government says civilian casualties during the US-led assault on Falluja have been minimal and that reports of a humanitarian crisis in the city are exaggerated.
"The ICRC is very worried about the humanitarian situation in Falluja"
ICRC spokeswoman, Geneva
But a spokeswoman for the International Committee of the Red Cross (ICRC) insisted in Geneva on Tuesday there were civilians still in the city, in need of food, water and medicine.
"The ICRC is very worried about the humanitarian situation in Falluja, because we are receiving information from families that are still there that the injured have no access to medical care," Rana Sidani said.
The ICRC did not know how many people were left in the shattered city of 300,000, but the Iraqi Red Crescent put the figure at around 150 families, she added.