United Nations Security Council ambassadors will spend the weekend conferring with their governments about American proposals for Iraq's future.
The US wants more international troops to share the burden
The United States, which hopes to broaden the international effort to stabilise the country, presented its plan for a multinational force at an informal Security Council meeting hosted by the UK mission in New York on Friday.
The draft resolution has already been criticised by France, Germany and Russia - countries which also opposed the US-led invasion of Iraq.
But the British ambassador to the UN, Emyr Jones Parry, said there was a clear determination among the 15 council members to find a common position.
The Americans have signalled their willingness to consider changes to the draft resolution, and are reported to be pushing for a quick vote on the draft by early next week.
DRAFT TEXT: MAIN POINTS
Reaffirms 'vital role' of UN
Calls for democratic elections
Seeks multinational force
Meanwhile, US President George W Bush is preparing to make a 15-minute national address on the situation in Iraq on Sunday evening amid a growing barrage of criticism at home.
Opposition Democrat politicians have accused Mr Bush of unnecessarily endangering the lives of American troops - dozens of whom have been killed in Iraq since the president declared major combat operations over - and jeopardising relations with international allies.
A White House spokesman, Scott McClellan, said the president's address would focus on progress made in Iraq so far and the country's needs for the future.
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.
Its key ally Britain, which has about 10,000 troops in Iraq, is sending a company of up to 150 soldiers from the 2nd Battalion Light Infantry to Baghdad from Cyprus this weekend ahead of an expected further deployment of more than 2,000 troops.
The BBC's Susannah Price at the UN says the Americans want to persuade countries such as India and Pakistan to bolster troop numbers in Iraq through a UN-authorised multinational force, with the US remaining in command.
These countries have all made clear their reluctance to send troops to Iraq without an international mandate.
The draft resolution also specifies that the UN should play a vital role in the political development of the country, helping the US-appointed Iraq Governing Council draft a programme for elections.
US 'prepared to listen'
Critics such as France and Germany say this does not go far enough and the UN needs to be central to the whole political process.
But US Secretary of State Colin Powell signalled American willingness to consider changes to the draft, saying that Washington would "listen to all of the comments coming in".
In a foreign policy speech at George Washington University, Mr Powell said: "We will try to adjust and adapt to those comments, as long as this is consistent with the overall goal."
He stressed that US forces in Iraq would "neither leave too soon nor stay too long".
The British ambassador to the UN said he did not believe anyone wanted the basic military or political arrangements to be changed.
"Nobody is attacking the essential structures," Mr Jones Parry said.
"Of course people want to see the political development. The way the UN actually insinuates itself in this process - that's up for debate, and all I'm telling you is that debate is taking place."