"Civilians continue to pay the ultimate price. This tragedy must be stopped and those responsible for civilian deaths must be held accountable," said Amnesty International
"It is clear from recent events in Falluja that the parties to the conflict have disregarded international humanitarian law. A full, independent and impartial investigation is needed now," said Amnesty International.
There are fears that the ceasefire may not hold for long and the population of Falluja may once again be caught in the fighting and face a humanitarian crisis.
The fighting in Falluja erupted when US Marines sealed off the city and launched military operations on 5 April to seek the arrest of those responsible for the killing, burning and mutilation of four US private security guards on 31 March.
After days of fighting a ceasefire was agreed on 11 April and negotiations began between representatives of the Iraqi Governing Council, religious clerics and representatives of the city of Falluja.
Thousands of Falluja residents fled the city, many towards Baghdad. In a press briefing on 13 April UNHCR announced that it had made available 3,500 blankets, 1,200 mattresses, five emergency health kits (benefiting over 50,000 people) and other equipment to cater for displaced people from Falluja in Baghdad.