Britain's ambassador to the UN has said that agreement is now close on an initial resolution calling for an end to the violence in Lebanon.
The UN's failure to stop the violence has angered many Lebanese
Correspondents say Britain, France and the US are nearing consensus on a two- resolution process to halt the violence and then work for a longer-term deal.
US presidential spokesman Tony Snow said the text of the first resolution could be finalised within days.
But the news comes amid a row between a senior UN official and the US.
"I'm confident that I think by tomorrow we'll be in a position to have discussion... on a text which actually takes us forward," said Sir Emyr Jones-Parry, Britain's ambassador to the UN.
He said the prospects of adoption of a resolution soon had "improved considerably".
The BBC's James Robbins says the agreement is a diplomatic breakthrough after weeks of transatlantic division, although there are no guarantees it can deliver an end to the fighting on the ground.
He says a first resolution could be passed on Friday or over the weekend.
An initial resolution is expected to call for an interim cessation of hostilities - although the details of this are not known.
The second would authorise a substantial multinational force as a buffer between the two sides, and set out details of a permanent settlement.
Our correspondent says the US has retreated from weeks of insistence that an interim ceasefire was unacceptable.
The UN spokesman on the Middle East, Ahmad Fawzi, said there was "very, very cautious optimism" that member states were moving closer.
The first resolution is expected to call for a cessation of hostilities
US ambassador to the UN, John Bolton, said there were differences in approach to the nature of the cessation of hostilities and ways of making it permanent.
But he said there was "near complete agreement on the fundamental political framework".
A meeting scheduled for Thursday to bring together nations likely to contribute to a multinational stabilisation force has been postponed for a second time.
Initially this was blamed on differences between France and the US, but correspondents say that it is now unnecessary until after an initial resolution is passed.
The other two permanent members of the UN Security Council, Russia and China, have not yet been involved in negotiations.
It also remains unclear whether Israel, Lebanon, Hezbollah, Iran and Syria would accept the solutions under discussion.
The diplomatic progress comes amid a war of words between the US and the UN's second highest official, a Briton who has previously been outspoken about the Bush administration's foreign policy.
In an interview published in the Financial Times newspaper on Tuesday, the Deputy Secretary-General of the UN, Mark Malloch-Brown, criticised the US and UK for seeking to take the lead in resolving the Israel-Lebanon crisis.
Mr Malloch-Brown has criticised US foreign policy before
"It's not helpful for it again to appear to be the team that led on Iraq," he said.
"This cannot be perceived as a US-UK deal with Israel. One of my first bosses taught me it's really important to know not just when to lead, but when to follow."
US State Department spokesman Sean McCormack responded in comments on Wednesday:
"We are seeing a troubling pattern of a high official of the UN who seems to be making it his business to criticise member states and, frankly, with misplaced and misguided criticisms."