US Secretary of State Colin Powell said he was "encouraged" by a meeting of the five permanent members of the UN Security Council in Geneva to discuss the future of Iraq.
Mr Powell said all five members were committed to giving authority to Iraqis and that the meeting threw up "points of convergence". However, he added, there had been difficulties also.
UN Secretary General Mr Kofi Annan said consensus among big five powers on Iraq's future was "essential and achievable".
Earlier, there appeared to be virtually no chance of a breakthrough emerging from the meeting
Washington, which has de facto control in Baghdad as the main occupying power, needs cash and troops from other nations but says it does not believe Iraqis can take power as quickly as European governments - especially France - are proposing.
Joining the US and France in Geneva for the talks were the foreign ministers of Britain - which backs the US stance - Russia and China, which are taking a low-key position.
French Foreign Minister Dominique de Villepin says Paris wants a text that provides for handing executive powers over to Iraqis, possibly within a month, and also provides for elections by next spring.
The United States says the French proposal is a recipe for chaos in Iraq, where the governing council has little clout. US Secretary of State Colin Powell said the proposal was "totally unrealistic" and the United States would reject it.
"I cannot anticipate us agreeing to any language that would buy into what Minister de Villepin has been saying," he told reporters on his way to Geneva last night.