The UN Human Rights Council, based in Geneva, Switzerland, had postponed a vote last Friday on a resolution that would have condemned Israel's failure to co-operate with a UN investigation into the December-January war.
Richard Falk on Palestinian leadership's support to defer UN vote on Goldstone report
Such a vote would have been one of many steps to bring Israel before a war crimes tribunal, something many Palestinians want to see.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said: "There's no doubt the public outrage over the decision by the PA to withdraw support for the Goldstone report continues several days after that decision.
"We saw today some of the more powerful images of the people here in Gaza turning against the Palestinian Authority president."
He said a rally was held and that dozens of people - mostly intellectuals as well as university students some of whom were relatives of the victims of the Gaza war - were in attendance.
"During the course of that rally, we heard some very strong condemnation of the PA president," he said.
"We saw a very offensive public gesture. Many of them had taken off their shoes and slapped the posters of the Palestinian president."
Yasser Abed Rabbo, Abbas' senior adviser, told the Voice of Palestine radio: "What happened is a mistake, but [it] can be repaired. We have the courage to admit there was a mistake."
Israel launched a major offensive on the Hamas-governed Gaza Strip in December 2008, saying it wanted to stop rockets fired by Hamas into its territory.
At least 1,400 Palestinians and 13 Israelis died during the three-week war, prompting a UN investigation headed by Richard Goldstone, a former South African judge.
Ahmed Gebreel, a Libyan government spokesman, said his country had requested the meeting "because of the seriousness of the report and because we think it's too long to wait until March".
Hussein Ibish, a senior fellow at the American Task Force on Palestine, told Al Jazeera it is possible Libya might try to put a draft resolution forward "but I think there is no chance of any consequential action being taken by the Security Council".
Palestinians, including members of Fatah, the party of Abbas, have strongly criticised the Goldstone vote postponement, holding him responsible for the decision.
Following Libya's request, the Palestinian Observer Mission at the UN has expressed "full support" for the move.
"We are welcoming Libya's step that they have asked the Security Council to meet to discuss the Goldstone report," Abbas told the AFP news agency in a telephone conversation from Rome, the Italian capital.
"Libya's step is supporting the Palestinian people's rights."
Palestine TV, the official television channel of the Palestinian Authority (PA), reported that Abbas would send Riyadh al-Malki, the Palestinian foreign minister, to New York to assist in the Libyan bid to have the council address the report.
The Security Council session, however, may not be enough to limit the political damage suffered by Abbas and Fatah.
Fawzi Barhoum, a Hamas spokesman, said that the controversy surrounding the Goldstone report could affect the Palestinian reconciliation deal which Egypt has said will be signed later this month.
"All the Palestinian factions, including Hamas, are angry at the [Palestinian] Authority after what happened with the Goldstone report and this could affect the arrangements for the [reconciliation] dialogue," he said on Wednesday.
"According to Egyptian arrangements up to now, the delegations are due to go to Cairo ... and Egypt is to fix the date of the signing of the deal."
It accuses Israel of using disproportionate force and deliberately harming civilians and alleges Hamas fired rockets indiscriminately at civilians in southern Israel.
Both Israel and Hamas have denied the allegations.