After a meeting with German Chancellor Gerhard Schroeder in Paris on Sunday, French President Jacques Chirac said the two leaders had heard about the changes in the draft that the US was seeking to pass in the United Nations.
But the two leaders decided to reserve their opinions on the reported changes for the time being.
"We are waiting to see it before commenting," Chirac said.
According to diplomatic sources in Paris, the US has begun circulating at UN headquarters in New York a new version of the resolution, after the earlier one was summarily rejected.
France, Russia, China – all veto-wielding permanent members of the Security Council - had criticized Washington's previous draft of the resolution.
"We are waiting to see it before commenting"
The main points of disagreement were over how soon political authority would be restored back to the Iraqis, as also over the size of the UN's role during the transition.
Schroeder said it was important to restore democracy and stability in order to give the Iraqi people a stake in the normalisation process.
Calling the previous version "insufficient and partial", Schroeder hoped the new draft resolution "has a new dynamic".
Though reluctant to loosen its grip over Iraq, US is keen to lessen its own burden.
It is seeking to pass the resolution in the UN so that other countries would get the sanction to contribute both troops and cash for Iraq's reconstruction.