Libya circulated a letter on Tuesday on behalf of the UN Arab group urgently seeking "an emergency meeting" of the council to consider the Goldstone report, Ibrahim Dabbashi, Libya's deputy ambassador, said.
The UN Human Rights Council, based in Geneva, Switzerland, postponed a vote last Friday on a resolution that would have condemned Israel's failure to co-operate with its investigation into the December-January war.
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.
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".
Palestinians, including members of Fatah, the party of President Mahmoud 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 also Fatah.
Reconciliation in jeopardy
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.
Richard Falk on Palestinian leadership's support to defer UN vote on Goldstone report
"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."
A day earlier, a senior Qatari foreign ministry official had said the Palestinians missed a rare chance by delaying the UNHRC vote.
Sheikh Khaled bin Jassem Al Thani, head of the ministry's human rights department, told Al Jazeera on Tuesday that the Palestinian representative to the council had requested a delay until the next meeting in March.
"The Palestinian decision was based on their wishes ... and member states could not take unilateral measures contrary to the wishes of the Palestinian Authority," he said.
"There were many countries that supported [the report and a vote] ... it could have been adopted, but I think that an opportunity was missed and it may not come back."