Britain and France, backed by the United States, distributed a revised text late on Tuesday to all 15 Security Council members that makes concessions to Russia and China.
But it still calls on Iran to suspend uranium enrichment efforts, which the West believes are a cover for bomb making.
John Bolton, the US ambassador to the UN, said on Tuesday: "We have reached agreement on the bulk of the text, so there was movement on all sides. And now we need to see whether we can cross this last bridge, but we're very close.
"We have been incredibly flexible. Incredibly flexible. I probably have never been more flexible."
The Security Council consults on Wednesday afternoon after the five powers meet again.
The council hopes the statement will be adopted then or at least be ready for approval early on Thursday when foreign ministers of the five permanent members and Germany meet in Berlin to discuss strategy on Iran.
Tools of isolation
In Washington on Tuesday, Condoleezza Rice, the US secretary of state, said Washington had "a number of tools" to isolate Iran and "if necessary, within the UN Security Council".
In London, Jack Straw, the British foreign secretary, sought to assure Russia and China that Security Council action would not lead to military strikes.
Straw said: "As to the possibility of this leading to another Iraq, it won't. I have made clear often enough that I don't regard military action as appropriate or indeed conceivable.
"Nor do I believe there would be any international consensus on that and I think Russia and China are well reassured on that."