JERUSALEM, March 19 (Reuters) - Israel's military was rocked on Thursday by Gaza war veterans' accounts of the killing of civilians and allegations that deep contempt for Palestinians pervaded its ranks.

The soldiers, alumni of a military academy, gathered last month to discuss their experiences in the 22-day Israeli offensive that ended in January, a campaign that Palestinians and human rights groups have said warranted war crimes probes.

Disclosing details of the session, the institution's director said the soldiers pointed to an atmosphere within the military of "unbridled contempt for, and forcefulness against, the Palestinians".

"They talked about unwarranted fire on Palestinian civilians. There was also talk of vandalism to property," Danny Zamir, head of the Yitzhak Rabin pre-military programme, told Israel Radio.

Defence Minister Ehud Barak responded to the accusations by repeating Israel's description of its armed forces as the most moral in the world. The military said its judge advocate-general ordered an investigation of the alleged incidents.

Excerpts from the veterans' discussion appeared on Thursday on the front page of the left-leaning Haaretz daily. It said the airing of the "dirty secrets" would make it more difficult for Israelis to dismiss such allegations as Palestinian propaganda.

It has been rare for Israeli soldiers to speak out about the killing of Palestinian civilians in the operation that Israel launched in the Hamas-ruled Gaza Strip in December with the declared aim of halting militants' cross-border rocket attacks.

WRONG TURN

One of the soldiers, an infantry squad leader, recalled an incident in which he said an army sharpshooter killed a Palestinian mother and her two children who turned the wrong way after troops ordered them out of their house.

"The platoon commander let the family go and told them to go their right. One mother and her two children didn't understand and went to the left ... The sharpshooter saw (them) approaching him, closer than the lines he was told no one should pass. He shot them."

The squad leader said most of the men under his command felt "the lives of Palestinians ... is something very, very less important than the lives of our soldiers, so as far as they are concerned, they can justify it that way".

Zamir said he conveyed the veterans' accounts to the Israeli military. Israeli leaders have said Hamas bore ultimate responsibility for civilian deaths because its fighters operated in crowded Palestinian areas.

Another squad leader who attended the academy said at the gathering that a company commander had ordered an elderly Palestinian woman shot as she walked on a road about 100 metres (yards) from a house that troops had taken over.

Describing vandalism carried out by soldiers, the squad leader said: "To write 'death to the Arabs' on the walls, to take family pictures and spit on them, just because you can -- I think this is the main thing, to understand how much the IDF (Israel Defence Forces) has fallen in the realm of ethics."

The Palestinian Center for Human Rights has put the Palestinian death toll during the war at 1,434 -- 960 civilians, 235 fighters and 239 police officers. Israeli officials have disputed the figures. Thirteen Israelis were killed.

Zamir said that while veterans at the alumni session had not directly taken part in war crimes, "they felt uncomfortable because they could not prevent them". (Editing by Samia Nakhoul)