The assembly announced Monday's delay at the request of Jordan, representing the Arab nations. Amman requested a vote for Tuesday on a revised resolution that is being negotiated.
The Palestinians had sought a vote in the 191-member assembly urging Israel obey the 9 July court opinion, but European Union states sought to include mention of the Middle East peace process in the resolution, said a European diplomat.
The announcement of the delay was followed by a testy exchange between the Israel's UN Ambassador Dan Gillerman and the Palestinians' UN observer, Nasir al-Kidwa.
Al-Kidwa said Gillerman was "hopeless" after the Israeli representative lashed out for being called to hear "a 30-second statement" about the postponement.
The Palestinian observer said the delay was to give member states a chance to read and digest a redrafted resolution. It also was an effort, he said, to get as large an agreement as possible for the measure.
No legal binding
An assembly vote, like the opinion of the International Court of Justice, is not legally binding, but both have symbolic value as international statements of support.
Only the 15-member Security Council can order the barrier to be torn down or impose sanctions. But the United States- Israel's staunchest ally - would almost certainly use its veto power to kill any such resolution.
Palestinians continue to resist
The concrete barrier, which towers eight metres in some parts, cuts off some of the most fertile and water-rich areas of the West Bank, divides villages and is preventing thousands of Palestinian farmers from reaching their land.
Palestinians fear the wall amounts to a land grab and will demarcate the borders of a future state. Israel claims the barrier is needed to keep out resistance fighters, a stance dismissed by human rights groups.
The court, as well as the Palestinians' draft resolution, urged the barrier be dismantled and reparations be paid to Palestinians harmed by its construction. But a defiant Israel has refused to recognise the world court ruling, saying it has no authority to deal with the issue and has ordered construction to go on.
Al-Kidwa was seeking the assembly vote to reinforce the court opinion that the Israeli fence violates international law.
Al-Kidwa has said nations should begin thinking about sanctions because of Israel's "negative response" to the court decision. He has said Palestinians will go to the Security Council despite the prospect of US veto.
In Brussels, the European Union's foreign and security policy chief, Javier Solana, scolded Israel on Monday for continuing the wall.
"Israel has the right to construct defensive walls in their own territory, but it does not have the same right to do it in other territories," he said.
But Israeli Foreign Minister Silvan Shalom's office said he was seeking European Union support in fighting a Palestinian attempt to secure UN sanctions if Israel refuses to accept the world court ruling.
US Ambassador John Danforth said on Friday the issue would not be resolved "in either the General Assembly or in court. It needs a political resolution."
A European diplomat, who asked not to be identified, said EU members were trying to broaden the assembly's resolution specifically to add mention of efforts seeking to resolve the Palestinian-Israeli conflict.
Danforth accused the draft resolution of moving away from the US-backed "road map" aimed at resolving the conflict.