Brazil's UN envoy Ronaldo Mota Sardenberg on Monday introduced the draft from the so-called G4, which calls for enlarging the Council from the current 15 members to 25 by creating six new permanent seats without veto power and four non-permanent seats.
The G4 countries are pressing for an early vote on the draft, which is co-sponsored by 23 countries, including current permanent member France, possibly as early as late this week.
Sardenberg said the security structure established in 1945 when the UN was created was "now glaringly outdated".
"The Security Council needs to undergo a thorough reform which includes an expansion of the category of permanent members in order to bring it in line with the contemporary world," he told the assembly.
He said such a reform would ensure a "better response to the evolving nature and characteristics of threats to peace as well as systematic and effective compliance with its decisions".
The draft does not spell out which countries would secure the new Council seats but diplomats said the six new permanent seats would go to the G4 and two African countries yet to be selected.
At present, Britain, China, France, Russia and the United States are the only permanent and veto-wielding members of the powerful UN body, which also has 10 rotating non-permanent members without veto power.
The proposed expansion of the Security Council is part of a broader plan to overhaul the United Nations, spearheaded by UN Secretary-General Kofi Annan.
World leaders will discuss the reform package at a summit in September before the annual general assembly.
"The Security Council needs to undergo a thorough reform which includes an expansion of the category of permanent members in order to bring it in line with the contemporary world"
Ronaldo Mota Sardenberg,
Brazil envoy to UN
Japan's UN envoy Kenzo Oshima meanwhile made it clear that the Security Council "needs to be expanded, both in its permanent and non-permanent categories, adding new members from developing and developed countries".
But Pakistan's UN ambassador Munir Akram expressed strong opposition to the G4 blueprint.
"We will not choose to anoint six states with special privileges and stamp ourselves as second class members in this organisation," he said, calling the plan "unequal" as it would give permanent membership to 11 states, "consigning 180 others to compete for 14 seats".
China's UN envoy Wang Guangya also voiced strong reservations.
"Most member states do not want to be forced to vote on a formula on which there is no broad consensus," he said.
"China is firmly opposed to setting an artificial timeframe for the Security Council reform and rejects the forcible vote on any formula on which there still exist significant differences."