Under the proposal, Israeli forces would only have to "start" withdrawing from southern Lebanon once a truce starts with the Hezbollah militia, a diplomatic source told AFP on condition of anonymity.
Meanwhile military chiefs from Southeast Asia's three mainly Islamic countries say they are willing to send about 2,000 personnel to any UN peacekeeping force for Lebanon.
Indonesian military chief Djoko Suyanto said that the forces from Brunei, Indonesia and Malaysia would be prepared while awaiting approval by the UN Security Council to be included under any peacekeeping contingent.
"The message that we want to convey is that the UN must know how serious these three countries are in preparing this mission," he said after talks with his Malaysian counterpart Mohammad Anwar and Brunei military chief Awang Halbi.
More than four weeks into the conflict, US and French envoys are thrashing out diplomatic differences which have held up a UN Security Council call for a ceasefire.
The major powers have reported slow progress in efforts to agree the wording of a truce call, despite mounting international impatience.
On one side, France wants a resolution to incorporate Lebanese demands that Israeli troops must leave Lebanon as soon as fighting stops. Lebanon has offered to deploy a 15,000-strong force in the south of the country.
The United States, Israel's major ally, and the Jewish state want Israeli troops to be able to remain there until an international force arrives, fearing that Hezbollah could retake control of the border zone.
According to one diplomat, France has proposed putting a paragraph in a new draft resolution saying: "Lebanese troops should start deploying in south Lebanon in coordination with UNIFIL as the Israeli forces start withdrawing behind the Blue Line."
The Blue Line is the unofficial border between Lebanon and Israel.
US still to accept proposal
The source said the proposal has also been put to the United States and presented to the other permanent members of the Security Council - Britain, China and Russia - but that it had not yet been accepted by the United States.
Diplomats said no vote on a resolution was now likely before Friday, at the earliest.
"My sense is that we are getting closer in the way of resolving some of this, but I don't want to underestimate the difficulties that we are trying to overcome," said US ambassador John Bolton after meeting the envoys from France, Britain, China and Russia.
The French UN ambassador, Jean-Marc de La Sabliere, called the meeting "useful" but commented "there are still some differences that have to be overcome -- and quickly."
French President Jacques Chirac hinted earlier that France may present its own resolution if there is no agreement with the United States.
Ambassador Bolton said the United States remains concerned about how to disarm and keep Hezbollah fighters out of positions to launch attacks on Israel.
He told reporters "everybody wants to see this (resolution) used to transform the situation in the region, which means fundamentally that we don't want Hezbollah to reinfiltrate the southern part of Lebanon."
Ambassador Bolton added: "The question remains how to have an effective security presence in the southern part of Lebanon as the Israeli forces withdraw, when that becomes appropriate."
The US ambassador said the Lebanese offer to deploy troops was "significant" and that it would be taken into account in the new draft, but did not say how.
France and the United States face strong Arab resistance to their current draft text, which does not specifically call for an Israeli withdrawal from Lebanon after any end to hostilities.
An Arab League delegation warned the Security Council on Tuesday there would be civil war in Lebanon if Israel's troops did not leave. The Arab ministers also criticised the delay in Security Council action.
US warns against escalations
While the talks went on, the United States warned Israel and Hezbollah against any "escalations" in the conflict, after Israel expanded its military operation against the militia.
"It's a message to all parties," White House spokesman Tony Snow said as the Lebanese Shiite militia threatened more attacks on the Israeli city of Haifa. "We want an end to violence and we do not want escalations."
Mr Snow also refused to predict when the UN Security Council would vote on a resolution.
"At this point, it's beyond any of us to come up with a firm prediction," he said. Last week, the White House confidently predicted UN action by Tuesday.
The French president said, meanwhile, that it would be "immoral" to give up trying to secure an immediate truce.
"It seems indeed that there are American reservations towards adopting the proposal" for a Lebanese deployment, president Chirac said after a meeting with top ministers on the conflict.
"If we fail to agree, we will have a Security Council debate at which each side will clearly reaffirm their position, including naturally France with its own resolution," he said.
Australian parliament
Meanwhile the Australian Greens have failed for a second time to convince the Senate to pass a motion calling for an immediate ceasefire in Lebanon and Israel.
Greens senator Kerry Nettle last night tried to get the Senate to agree on a formal motion calling for an end to the conflict.
Labor refused to support the move, arguing it was simplistic to reduce a serious matter of war and peace to a yes-or-no Senate motion, criticising it as "petty political point scoring".
Senator Nettle today tried to get the Senate to agree on an amended motion supporting any ceasefire in the Middle East and calling on the Australian government to do the same.
But the coalition and Labor combined to defeat the motion 52-7.