"We urge you to oppose this resolution and, should it come to a vote, to vote against it," said Shirin Tahir-Kheli, a senior adviser to US Secretary of State Condoleezza Rice, on Tuesday.
The US diplomat joined a number of countries, including Canada, Uruguay, New Zealand and Russia which spoke against the G4 text, which calls for enlarging the council from 15 members to 25 by creating six new permanent seats without veto power and four non-permanent seats.
The G4 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.
Noting that the G4 countries were friends of Washington, Tahir-Sheli said: "We reiterate our willingness to work with them and other countries in the effort to achieve Security Council enlargement via a plan that is supported by the vast majority of UN members, and which results in a stronger, more effective Security Council."
"Unfortunately, however, the timing and substance of the proposed (G4) resolution does not accomplish these ends," the US diplomat said.
In the face of spirited opposition, the G4 blueprint is unlikely to muster the required two-thirds majority vote in the General Assembly - 128 votes out of 191 - to change the make-up of the council.
It has sharply divided the 191-member assembly and led the African group at the UN and a so-called "United for Consensus" group led by Pakistan, Argentina, Italy and Mexico to circulate competing proposals.
At present, Britain, China, France, Russia and the United States are the only permanent and veto-wielding members of the Security Council, which also has 10 rotating non-permanent members without veto power.