The US and Britain have presented a new resolution to the UN Security Council endorsing the transition of power to the Iraqi interim government.
The US hopes Iraq's new leaders will speed the diplomatic process
It sets a date for the end of the mandate of US-led troops and stresses the new government will have full control over Iraqi security forces.
The new interim president and cabinet were sworn in on Tuesday in Baghdad.
China, France and Russia objected to the first draft because it did not give Iraqis control over military affairs.
The new resolution does not change the wording on this point, but it does set a time frame for the force to withdraw.
IRAQ SELF-RULE TIMETABLE
30 June: Handover from Coalition Provisional Authority to interim government
End of Jan 2005: Elections to National Assembly
Autumn 2005: New constitution voted on in referendum
December 2005: Full elections for new government
January 2006: Directly elected government takes office
This UN mandate will end when a fully representative government takes power after democratic elections are held at the end of 2005.
BBC News Online world affairs correspondent Paul Reynolds says this is being widely intepreted as meaning that the force would withdraw then, but it would be open to the elected government to ask some at least of the force to stay.
The UN ended a first round of consultations over the resolution on Tuesday.
But the Security Council is not expected to reach a decision until talks have been held with more UN officials and with members of the Iraqi interim government.
The new Foreign Minister, Hoshiyar Zebari, is expected to arrive in New York on Wednesday and meet UN Security Council members on Thursday.
President Bush has said he does not believe much progress will be made before then.
However, the BBC's Jon Leyne in Washington says the US administration is trying to move the diplomatic process on as quickly as possible.
The revised text is designed to show that the new Iraqi government will have full sovereignty and control over its own affairs after 30 June, our correspondent says.
The new draft also makes it clear that Iraqis will have control over their own resources.
It also highlights the Iraqi interior ministry's control over police forces.
But the resolution still retains some controversial points.
It says the multi-national force has the authority to take all necessary measures to maintain security and does not mention whether Iraqis will be able to veto any military operations.
Some Security Council members want the resolution to state that the Iraqi government will be consulted about military operations being carried out by the Americans but the coalition says the relationship will be spelt out in letters between the Iraqi government and the force.
The British ambassador to the UN, Emyr Jones Parry, said he hoped the new resolution will be swiftly adopted.
"We think our amendments were quite well received today in the council," he said.
Discussion of the UN resolution came as the new Iraqi government was sworn in following the surprise resignation of the Governing Council, which had been expected to continue in office until the handover.
KEY CABINET POSTS
Interior minister: Falah al-Naqib
Foreign minister: Hoshiyar Zebari
Defence minister: Hazim al-Shalaan
Finance minister: Adel Abdul Mehdi
The dramatic change of leadership occurred just hours after Ghazi Yawer was named as Iraq's president.
At the swearing-in ceremony, Mr Yawer said his goal was to make Iraq one nation, "without murderers and criminals".
He said that while he wanted the US occupation of Iraq to end as soon as possible, for now coalition forces would remain in place.
He expressed gratitude for what the coalition forces had done thus far in Iraq.
Mr Bush described the developments as "a very hopeful day for the Iraqi people and the American people", and praised the role of the UN for its input in the formation of the government.