Israel is accused of bombing civilian buildings without military necessity
The Palestinians have urged the UN to act to punish Israel for its offensive in the Gaza Strip last winter.
The move reverses a Palestinian decision to defer action on a UN report that accuses both Israel and Hamas of war crimes during the conflict.
Israel rejected the report as biased during a UN Security Council debate.
Meanwhile, UN chief Ban Ki-moon urged "credible" investigations by Israel and the Palestinians into allegations of war crimes during the conflict.
"The world has for too long witnessed Israel's impunity, knowing well that this has been repeatedly fuelled by the lack of punishment and accountability," Palestinian Foreign Minister Riad al-Malki said during a Security Council debate on the Middle East on Wednesday.
"The tragic consequences have been suffered by generations... We must break this obscene cycle," the minister added.
Mr Malki's comments represent a sharp policy reversal, says the BBC's Barbara Plett at UN headquarters in New York.
Under US pressure, the Palestinians had earlier agreed to defer action on the UN report by veteran South African judge and war crimes prosecutor Richard Goldstone, but that led to a public outcry, our correspondent says.
Meanwhile, Israel's envoy to the UN, Gabriela Shalev, said the UN report was biased and favoured terrorism.
"For those of us who seek to resume the peace process in the Middle East, debating the Goldstone in the Security Council is but a tale full of sound and fury, signifying nothing.
"If Israel is asked to take further risks for peace, the international community must recognise our right to self-defence," Ms Shalev said.
The Americans also said the report had an unbalanced focus on Israel, and opposed it being taken up by the Security Council, our correspondent says.
Separately, the UN Secretary General Ban Ki-moon urged "credible" investigations by both sides into the conduct of the Gaza conflict "without delay".
"He [Mr Ban] hopes that such steps will be taken wherever there are credible allegations of human rights abuses throughout the world," UN Undersecretary General Lynn Pascoe told the Security Council.
Libya, a rotating member of the 15-seat Council, had been seeking a special session of the UN's top decision-making body to discuss the report, but agreed to bringing the monthly session on the Middle East ahead by one week.
Palestinian Authority President Mahmoud Abbas is seeking a special session of the UN Human Rights Council to vote on the report.
The Goldstone report accuses Israel of using disproportionate force and deliberately harming civilians during the 22-day conflict which began on 27 December 2008.
Hamas militants are accused of indiscriminate rocket fire at Israeli civilians.
The report urges the Security Council to refer allegations to the International Criminal Court if either side failed to investigate and prosecute suspects.
Israel has rejected the evidence, saying it has already investigated its troops' conduct, clearing most of the subjects of wrongdoing. Hamas also denied committing war crimes.
Israeli military action destroyed thousands of homes, hundreds of factories and 80 official buildings in Gaza.
Palestinians and human rights groups say more than 1,400 people were killed in the violence between 27 December 2008 and 16 January 2009, more than half of them civilians.
Israel puts the number of deaths at 1,166 - fewer than 300 of them civilians. Three Israeli civilians and 10 Israeli soldiers were also killed.