By Bridget Kendall
BBC News, New York
The UN draft may call for a phased withdrawal of Israeli forces
Work at the UN on revising a draft resolution to try to end the violence in the Middle East continues - so do frantic phone calls across the Atlantic.
But there is now renewed urgency and cautious optimism in New York that differences on this elusive text have narrowed.
US ambassador to the UN John Bolton said some areas of disagreement with the French had been closed and a vote on Friday was entirely possible.
UN Secretary General Kofi Annan said adopting a resolution by the end of the week ought to be achievable. In Paris French Foreign Minister Philippe Douste-Blazy said he hoped a deal was imminent.
The British Foreign Secretary Margaret Beckett has already broken into her holiday to fly to New York to take part in negotiations.
In London a spokesman for Prime Minister Tony Blair said that did not mean a vote was now certain - Mrs Beckett's travel plans reflected her and Mr Blair's concern that a final push was needed to seal the deal and make real the potential for a vote to be passed in the next 24 hours or so.
In Washington the State Department said Secretary of State Condoleezza Rice was also prepared to travel to New York if necessary, either for a vote or discussions on last minute details.
The new deal appears to centre on a plan to introduce Lebanese troops into the border region, strengthen the existing UN force, Unifil, and give it a tougher mandate, while at the same time Israelis begin a phased withdrawal.
That would require the consent of the Lebanese government - and Hezbollah - as well as the Israelis.
But the first step is agreement from the French and the US - the key negotiators.
If they emerge with an agreed draft text, then the scene would be set for a possible vote in the next day or so.
Any deal would of course be a compromise.
According to officials, the lead force would be the Lebanese army - to meet Lebanese concerns that the process should increase their control over their own territory, not hand it over to foreign troops - or worse still leave in place Israeli forces.
But to meet Israeli concerns that any force in southern Lebanon should be strong enough to prevent Hezbollah from returning, the Lebanese army would be accompanied by a UN force, based on Unifil but boosted by new international troops and with a new mandate.
A month into the conflict many parts of Lebanon have been devastated
Whether France would provide troops for this force is not yet clear. Diplomats said that decision was up to President Chirac.
But sources said other nations were also in discussions, including Spain, Italy and possibly Australia, to see if they might participate, depending on the circumstances of the deal.
The strengthened mandate of the UN force is also a potential point of contention.
There is broad agreement in New York that the new force would have to upgrade the status of the current Unifil mission to a "Chapter Seven" mandate - to give troops the right to use force to defend themselves and carry out their mission to secure the area.
That in turn would require the consent of the Lebanese government, which of course includes Hezbollah ministers.
Apparently the UN secretary general has added his weight to a request to the Lebanese prime minister. Without that agreement, the whole deal could founder.
As for how soon this plan could become a reality on the ground, if all agree, that too is a pivotal question.
In the first place it depends on getting the UN vote through.
Though frustrated diplomats in New York all seem to agree they would like a deal done by this weekend, that does not mean they have the power to achieve it.
Last minute objections by any of those involved on what at first appears a minute detail could hold it up for hours, or days, as the last week's roller coaster ride of frustrated expectations has illustrated.
But if a vote can be achieved soon, and a cessation of hostilities could be agreed, and Israel and Hezbollah really do agree to stop attacking each other, then one official source said the deployment of the first troops on the ground might happen in a matter of days.
Bridget Kendall will be presenting our global phone-in programme, Have Your Say, live from New York on Sunday 13 August at 1500 BST. If you would like to take part please send your comments to firstname.lastname@example.org