Abbas' reversal came under heavy U.S. pressure and means no further international action is likely for at least six months.
At issue is a recent U.N. report that alleges both Israel and Hamas committed war crimes in three weeks of fighting.
The 47-member U.N. Human Rights Council had been expected to vote this week on a resolution to refer the report to the U.N. General Assembly, moving one step closer to possible prosecutions.
However, the Palestinians agreed Friday to drop their support for the resolution after intense U.S. lobbying. With the Palestinians out of the picture, the council's Arab and Muslim states followed suit. A vote was delayed until March, meaning the report will now lie dormant while the global body decides what, if anything, to do with it.
In Gaza, the Islamic militant Hamas branded political rival Abbas and members of his West Bank government as traitors.
"This ... represents a betrayal of the Palestinian cause and confirms the extent of the collaboration between Abbas and his aides with the Zionist enemy, against the Palestinian people," said Hamas lawmaker Mushir al-Masri.
The West Bank-based human rights group Al Haq said Abbas has failed to stand up for his people.
Abbas aide Nimr Hamad defended the move as a mere delay, to allow more time to gather support for the report, written by respected jurist Richard Goldstone. "The report wasn't withdrawn," said Hamad. "It's still there."
A senior U.S. official, speaking on condition of anonymity, said Washington exerted strong pressure to persuade the Palestinian leadership that going ahead with the resolution would harm the Middle East peace process. The Obama administration wants to revive Israeli-Palestinian peace talks that broke off last year, though Abbas rejects a return to negotiations without an Israeli settlement freeze.
The 575-page Goldstone report accused Israel of using disproportionate force and failing to protect civilians while calling Hamas' firing of rockets at civilian areas in southern Israel a war crime.
It recommended that the U.N. Security Council in New York require both sides to carry out credible investigations into alleged abuses during the conflict _ in which 13 Israelis and almost 1,400 Palestinians, including hundreds of civilians, were killed.
Israel has vehemently rejected the war crimes allegations. The U.S. has called the report deeply flawed and said it disagrees with many of its assessments.
U.S. Assistant Secretary of State Michael H. Posner said Friday that the delay could allow Israelis and Palestinians time to review the report's findings themselves. "I think it actually provides some opportunity for there to be a more meaningful discussion of the merits of the report by both sides," he said.
However, Israel has repeatedly rejected demands by human rights groups, both at home and abroad, that it launch an independent investigation. The groups have said the army's debriefing of troops and two dozen military police investigations into alleged violations by soldiers fall far short of an independent probe.
The London-based group Amnesty International said Friday that it fears deferring the vote is a sign of a "lack of political will" to deal with violations of international law. "However, this deferral provides both the Israeli government and the Hamas de facto administration in Gaza with one last opportunity to conduct independent investigations," Amnesty said.
Goldstone said his findings stand and expressed hope that the report is not being buried.
"The deferral of six months does not mean impunity for serious violations will continue," he said. "I reiterate that providing, and ot denying, justice to victims of violations is the only path to durable peace."
Associated Press Writer Frank Jordans contributed reporting from Geneva.