The United States is facing growing opposition to its revised proposals on the future of Iraq.
Security in Iraq is a problem despite the US presence
Russian President Vladimir Putin said Moscow was "not satisfied" with the latest draft resolution presented to the United Nations, echoing criticism from France and Germany.
The draft says the body should strengthen its role in Iraq, calls for the political transition to be as quick as possible, and urges member states to contribute to a multinational force.
US Secretary of State Colin Powell defended what he described as a "good resolution" and said he was "anxious" to get specific suggestions from the critics.
US DRAFT'S KEY POINTS
Bigger UN role
Progressive handover of power to Iraqis
New constitution and elections
Multi-national force under unified command
Effective Iraqi police and security forces
Full range of loans for reconstruction
He said Washington remained committed to transferring power to Iraqis but had to be cautious.
"We believe we have an obligation to turn it [authority] over to a responsible government that is able to handle that responsibility and not just turn it over because two or three months have passed and we are anxious to remove a burden from ourselves," he said.
BBC diplomatic correspondent Barnaby Mason says the US draft does not say how the UN's role would be stronger, while other clauses imply that the US-led coalition will continue to have the predominant voice.
UN Secretary-General Kofi Annan has been reported as saying that the resolution would not allow the UN to play a proper role in Iraq.
Like other critics, Mr Annan favours the formation of a provisional Iraqi Government, which would draft a constitution and hold elections.
Giving the responsibility to the Iraqis, he argues, would reduce the sense of foreign occupation and with it the resistance.
The Bush administration is under growing political pressure at home but it is not clear yet whether this will incline it to make concessions in the Security Council, our correspondent adds.
France has said the draft does not incorporate the changes it has been advocating - a rapid transfer of power to Iraqi authorities and a strong role for the UN.
"Our first impression is that our concerns are not reflected in the revised US draft resolution except in a very limited way, and that this text does not contain the change of approach that we are urging," foreign ministry spokesman Herve Ladsous said.
Earlier on Friday, Mr Putin said: "We are not satisfied with the draft by our American partners, though they are trying to find a compromise."
And the main Iraqi Shiite Muslim group also criticised Washington's draft, Egyptian state media reported.
Reda Jawad Taqi, a representative of the Supreme Council for the Islamic Revolution in Iraq (SCIRI), said the draft was "weak" because it did not include "a deadline and a timetable for the withdrawal of coalition forces," Mena news agency said.
French on board
Mr Annan's comments - that the draft was "not going in the direction" he wanted - may delay the adoption of a new resolution, our correspondent says.
Its critics may also be encouraged in their opposition by the failure of an American-led team so far to find any Iraqi weapons of mass destruction.
The US administration is under pressure at home and abroad
The US has said it wants to get a resolution passed before an international conference to raise money to help rebuild Iraq later this month.
The Security Council is due to meet again on Monday for further discussions.
France has said that despite its misgivings, it will not veto a resolution when it is put to a vote.