John Ging, head of the UN Palestinian refugee agency in Gaza, said: "It's about accountability [over] the issue of the appropriateness of the force used, the proportionality of the force used and the whole issue of duty of care of civilians.
"We don't want to join any chorus of passing judgment but there should be an investigation of any and every incident where there are concerns there might have been violations in international law."
The Israeli military are accused of:
• Using powerful shells in civilian areas which the army knew would cause large numbers of innocent casualties;
• Using banned weapons such as phosphorus bombs;
• Holding Palestinian families as human shields;
• Attacking medical facilities, including the killing of 12 ambulance men in marked vehicles;
• Killing large numbers of police who had no military role.
Israeli military actions prompted an unusual public rebuke from the International Red Cross after the army moved a Palestinian family into a building and shelled it, killing 30. The surviving children clung to the bodies of their dead mothers for four days while the army blocked rescuers from reaching the wounded.
Human Rights Watch has called on the UN security council to set up a commission of inquiry into alleged war crimes.
Two leading Israeli human rights organisations have separately written to the country's attorney general demanding he investigate the allegations.
But critics remain sceptical that any such inquiry will take place, given that Israel has previously blocked similar attempts with the backing of the US.
Amnesty International says hitting residential streets with shells that send blast and shrapnel over a wide area constitutes "prima facie evidence of war crimes".
"There has been reckless and disproportionate and in some cases indiscriminate use of force," said Donatella Rovera, an Amnesty investigator in Israel. "There has been the use of weaponry that shouldn't be used in densely populated areas because it's known that it will cause civilian fatalities and casualties.
"They have extremely sophisticated missiles that can be guided to a moving car and they choose to use other weapons or decide to drop a bomb on a house knowing that there were women and children inside. These are very, very clear breaches of international law."
Israel's most prominent human rights organisation, B'Tselem, has written to the attorney general in Jerusalem, Meni Mazuz, asking him to investigate suspected crimes including how the military selects its targets and the killing of scores of policemen at a passing out parade.
"Many of the targets seem not to have been legitimate military targets as specified by international humanitarian law," said Sarit Michaeli of B'Tselem.
Rovera has also collected evidence that the Israeli army holds Palestinian families prisoner in their own homes as human shields. "It's standard practice for Israeli soldiers to go into a house, lock up the family in a room on the ground floor and use the rest of the house as a military base, as a sniper's position. That is the absolute textbook case of human shields.
"It has been practised by the Israeli army for many years and they are doing it again in Gaza now," she said.
While there are growing calls for an international investigation, the form it would take is less clear. The UN's human rights council has the authority to investigate allegations of war crimes but Israel has blocked its previous attempts to do so. The UN security council could order an investigation, and even set up a war crimes tribunal, but that is likely to be vetoed by the US and probably Britain.
The international criminal court has no jurisdiction because Israel is not a signatory. The UN security council could refer the matter to the court but is unlikely to.
Benjamin Rutland, a spokesman for the Israeli military, said an international investigation of the army's actions was not justified. "We have international lawyers at every level of the command whose job it is to authorise targeting decisions, rules of engagement ... We don't think we have breached international law in any of these instances," he said.