Annan called on the five permanent Security Council members to hammer out an agreement even as the 15-member Council held their first informal talks on the proposal.
"I have suggested to the permanent five foreign ministers that they meet with me to explore a common ground and the way forward," Annan said on Friday.
"And I hope that meeting will take place in the not too distant future," he added.
The dispute is over a new US draft resolution calling for a UN multinational force in Iraq. It also gives the UN a role in writing a constitution leading to elections.
But many countries, in particular France, Germany and Russia, are wary of the proposal which would leave the US in ultimate control.
Having initially opposed the war, they suspect the US is seeking to pass on to others the mess they have inherited in Iraq.
"I have suggested to the permanent five foreign ministers that they meet with me to explore a common ground and the way forward"
Kofi Annan, UN Secretary General
French President Jacques Chirac and German Chancellor Gerhard Schroeder have harshly criticised the US resolution and have demanded a timetable for the US occupation to end.
Stung by the rejection, US Secretary of State Colin Powell has asked them to make specific proposals.
"If you don't like it in this particular form and you want to see something different, then make a proposal in addition to an editorial comment," Powell said.
France is expected to produce amendments early next week, its diplomats said.