The report calls on both Israel and the Palestinians to investigate accusations of human-rights violations during the 22-day conflict in December and January.
The debate at the General Assembly, which began on Wednesday, was called for by the Arab UN group, with the backing of the 118-member Non-Aligned Movement (Nam).
Most of criticism in the report, compiled by a fact-finding panel led by Richard Goldstone, a South African judge, was directed towards Israel's conduct during the offensive, in which human rights organisations say about 1,400 Palestinians - many of them women and children - were killed.
Thirteen Israelis, including three civilians, were killed over the course of the war.
Al Jazeera's Kristen Saloomey, reporting from the UN in New York, said on Wednesday: "The Palestinians put forward this resolution with several co-sponsors knowing that they have the support to have it passed in the General Assembly.
"This is really an attempt to keep the Goldstone report alive. The resolution endorses the report and also attempts to force it upon the Security Council, by getting the secretary-general involved."
Riyad Mansour, the Palestinian observer to the UN, said the report concluded that the Israeli military onslaught "was planned in all of its phases as a deliberately disproportionate and systematic attack aimed at punishing, humiliating and terrorise the Palestinian civilian population".
Mansour warned that efforts by Israel and its supporters to discredit the UN report and its authors would not deter Arab states from following up the recommendations "in all relevant international forums, including the Security Council and the International Criminal Court, until the realisation of justice with the accountability of the perpetrators of these crimes and violations".
Gabriela Shalev, Israel's UN ambassador to the UN, hammered Wednesday's debate at the UN as "yet another campaign against the victims of terrorism, the people of Israel".
"The Goldstone report and this debate do not promote peace. They damage any effort to revitalise negotiations in our region. They deny Israel's right of self-defence," she told the assembly.
"From its inception in a one-sided mandate, the Gaza fact-finding mission was a politicised body with predetermined conclusions," she added.
US House vote
The US House of Representatives on Tuesday dismissed the report as being "irredeemably biased" against Israel.
The house voted in favour of a non-binding resolution calling on Barack Obama, the US president, to maintain his opposition to the report.
Goldstone last week sent a letter to the US House of Representatives saying that the text of the US resolution had "factual inaccuracies and instances where information and statements are taken grossly out of context".
He offered several rejections and clarifications of the ideas expressed in the resolution.
In response to Goldstone's criticism, three parts of the resolution were amended on Tuesday to clarify that Goldstone had sought an expansion to the commission's mandate so that his team could investigate claims that Hamas had violated international law during the Gaza war.
The Goldstone report accused Israel of using "disproportionate force" and of deliberately targeting civilians.
The report called for cases to be referred to the ICC in The Hague if Israel and Hamas do not investigate the war crimes allegations against them within six months.
Hamas has agreed to hold such an investigation, but Israel has not.