US officials say a compromise has been reached among UN Security Council members over a new resolution on Iraq.
The issue of control of foreign troops has held up agreement
The US and the UK agreed to add text that the US-led forces would consult the Iraqi interim government on major military actions.
This was a key demand by France - the earlier draft said the issue was dealt with in an exchange of letters between US and Iraqi officials.
The US says it now expects a unanimous backing of the resolution on Tuesday.
The US ambassador to the UN, John Negroponte, said Washington and London made a major effort to take the views of various delegations into account during the closed door consultations.
"We are putting it to a vote on Tuesday afternoon," Mr Negroponte told reporters during a pause in the discussion.
The French ambassador to the UN, Jean-Marc de la Sabliere, said there had been a lot of improvements and "the text is going in the right direction now".
He said he would transmit the text to Paris and wait for further instructions.
The German ambassador to the UN, Gunter Pleuger, said they had found a compromise and Germany - which alongside with Algeria backed the French amendment - "can live with that".
Speaking to the Security Council before it began discussing the draft, UN Iraq envoy Lakhdar Brahimi said it would take eight months from the time of forming an interim government before credible elections could take place.
Briefing the council on the results of his fact-finding mission in April, Mr Brahimi stressed that Iraq's structural and security problems would take years, not months, to overcome.
The US rejected France's demand that would have given Iraq a virtual veto over major coalition forces in Iraq after the 30 June handover.
But later the text was amended to reflect US-Iraqi military arrangements "to reach agreement on the full range of fundamental security and policy issues, including policy on sensitive offensive operations".
Before the discussions in New York, French Prime Minister Jean-Pierre Raffarin told French television the resolution was "evolving in the right direction", but added: "We want to see it evolve a little further."
Russian deputy foreign minister Yuri Fedotov said the draft resolution was "really improved", although some questions remained.
Earlier, US National Security Adviser Condoleezza Rice said she expected a vote on the resolution within days, though a number of elements were being finalised.
"I think it's fair to say that the spirit moving forward is very good, that people are working very hard at it and that there's
a general sense that this is going in a very positive direction and should reach a conclusion very soon," she said.
'Full range of issues'
The newly appointed Iraqi Prime Minister, Iyad Allawi, and US Secretary of State Colin Powell had promised in the letters to the Security Council to reach agreement on policy for dealing with sensitive offensive military operations.
But they have not spelled out whether the Iraqis have to give their consent to each operation, or what would happen if they did not agree.
In his letter, Mr Allawi repeats his request that foreign troops stay "until we are able to provide security for ourselves".
The letter says a ministerial body will be established to "co-ordinate [with the multinational force] on all security policy and operations issues".
In his letter, Mr Powell pledges to co-operate with Iraqis "on the full range of fundamental security and policy issues, including sensitive offensive operations".
The fourth draft of the resolution states that the mandate of the multinational force will expire after elections are held in Iraq, no later than 31 January 2005.