Resolutions passed by the assembly reflect world opinion but are not legally binding like those of the council, where the United States has regularly blocked resolutions it believes are unfairly critical of close ally Israel.
US ambassador John Negroponte used the council veto, held only by the five permanent members Britain, China, France, Russia and the United States, to shoot down the measure sponsored by the council's only Arab member, Syria.
The United States last month killed another council resolution criticising Israel for its threats to expel Palestinian leader Yasir Arafat from the occupied West Bank.
The apartheid wall separates many Palestinians from their farmlands and divides villages. It also slices off water-rich lands. Palestinians fear the barrier is an Israeli effort to demarcated the borders of a future Palestinian state.
Israel says it is trying to stop Palestinian activists from crossing into Israel to carry out resistance attacks.
Palestinian UN representative Nasir al-Kidwa said that in addition to a resolution on the barrier, the assembly would also be asked to vote on another measure to request a legal judgment on the barrier from the World Court.
International criticism for the wall is mounting.
On Saturday, 25 October, the Washington-based Peace and Justice Foundation is holding the Washington Conference on Civil Liberties in America. Its organisers said the issue of the barrier and Israel's occupation would be addressed.
The Council for Advancement of Arab-British Understanding (CAABU), a British-based group aimed at improving Arab-British ties, has urged constituents to write their members of parliament asking them to sign the Early Day Motion 1689.
The EDM, which was earlier tabled, has 98 MP signatures. CAABU said it would be a clear sign to Downing Street 10 if it received over 100 signatures.