The United States is presenting its plan for a multinational force in Iraq to the UN Security Council - but the draft resolution has already been criticised by France, Germany and Russia.
The US wants more international troops to share the burden
The Americans are reported to be pushing for a quick vote on the draft, by early next week.
But the pressure for changes to the document means the debate will probably be extended, the BBC's David Bamford reports from New York.
The 15 Security Council members are meeting informally at the British mission to the UN, a short distance from the UN headquarters.
US Secretary of State Colin Powell signalled that Washington was ready to take its UN partners' views on board.
"We'll listen to all of the comments coming in, we will try to adjust and adapt to those comments, as long as this is consistent with the overall goal," he said in a foreign policy speech at George Washington University.
He stressed that US forces in Iraq would "neither leave too soon nor stay too long".
DRAFT TEXT: MAIN POINTS
Reaffirms 'vital role' of UN
Calls for democratic elections
Seeks multinational force
America's new resolution was discussed on Thursday by ambassadors of the five permanent members - China, France, Russia, the UK and US.
France and Germany want the UN to play a much larger role in Iraq and to prepare the way for a new Iraqi government as quickly as possible.
Our correspondent says the majority of Security Council members share their doubts, and the Americans are on the defensive.
However, the US plan does not cede any political or military control or set out any time frame for elections.
Later on Friday, the Security Council will hold a formal debate on Iraq, examining its security problems, exacerbated by a spate of devastating bomb attacks targeting the UN and Shia Muslims as well as coalition forces.
Russia seeks changes
Russia on Friday voiced cautious support for the US proposals, saying they reflected the principles that it had championed.
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But Russian Foreign Minister Igor Ivanov said the draft resolution needed to be improved.
"The US draft is moving toward principles (supported by Russia) but for them to be outlined (in the resolution) in full, the document needs very serious work," he said.
The US badly needs a resolution that will, in the eyes of India, Pakistan, Turkey and others, legitimise their participation in the faltering security operation, our correspondent adds.
These countries have all made clear their reluctance to send troops to Iraq without an international mandate.
France is drawing up a list of proposed changes to the American resolution which it believes would accelerate the handover of power to Iraqis and bolster the UN's influence in Iraq.
The French and others are determined to make it clear the UN is in no way legitimising the US decision to go to war against Iraq, our correspondent says.
Many states also want the UN role in the political process to be put on a much firmer basis.
European Union foreign ministers are attending a meeting in Italy at which the security situation in Iraq is under discussion.
Most EU countries have held back from offering to send troops, although Britain is considering increasing the number of soldiers it has deployed.
The US wants another 10,000 foreign troops to be deployed in Iraq as part of the multinational force called for in the draft resolution.
But Australia, which sent 2,000 troops to join the coalition assault on Baghdad, has ruled out any increased participation.
Prime Minister John Howard said his country would not be sending peacekeepers to Iraq, even if the UN backed the idea of a multinational force.