A key finding of the UN report, head by Richard Goldstone, a South African judge, was that Israel used disproportionate force in response to repeated rocket attacks by Gaza-based fighters and failed to take adequate measures to protect civilians during its onslaught.
In the report, published in September last year, Goldstone recommended that both sides face possible prosecution before the International Criminal Court in The Hague if they failed to conduct credible, independent investigations within six months.
Referring to Friday's UN vote, Mansour said: "We expect a higher number of votes in favour of the [non-binding] draft resolution."
Last November, the 192-member assembly overwhelmingly passed a similar resolution calling for credible, independent investigations of the war crimes charges by February 5, with 114 voting in favour, 18 against, and 44 abstaining.
Many European Union countries, including Britain, France, Sweden and Spain, abstained after failing to secure amendments to the text, including one that would have dropped references to possible Security Council action if findings by the UN enquiry panel were not implemented.
Israel, which had strenuously opposed the text and the UN report which it endorsed, voted against as did its staunchest ally, the United States, along with Australia and a few European countries.
"I think the great majority of European countries will vote in favor this time, although there might be a few abstentions," Mansour said.
Several European diplomats confirmed that many EU members planned to approve the Palestinian text as they view it as relatively mild.
The draft again calls on the Israelis and the Palestinians "to conduct investigations that are independent, credible and in conformity with international standards".
It asks Ban Ki-moon, the UN secretary general, to report back to the assembly "within a period of five months on the implementation of the present resolution, with a view to the consideration of further action, if necessary, by the relevant UN organs and bodies, including the Security Council".
Israel, in a recent report on the allegations, denied violating international law, but admitted "tragic results" due to the "complexity and scale" of conducting a military operation in a heavily populated area.
| Goldstone said Israel used 'disproportionate force' during its war on Gaza [EPA]
It also said that two Israeli senior officers, a brigadier general and a colonel, had been disciplined for the firing of white phosphorus shells toward a UN compound.
A similar report from the Palestinian side said a commission of five well-known judges and legal experts had been set up to look into allegations of war crimes on its side during the conflict.
Mansour expressed hope the Palestinian side will be able to submit "a substantive report" within the next five months.
"If the Israelis continue to refuse an independent probe, they will then be isolated and this may pave the way for pressure on the Security Council to act," he said.