The US and France have agreed the wording of a UN resolution to end the fighting between Israel and Hezbollah.
As the violence goes on, the UN hopes diplomacy can end the crisis
It calls for a "full cessation of hostilities", demanding that Hezbollah halt all attacks and Israel stop all offensive military operations.
A BBC correspondent at the UN says the wording would allow Israel some freedom if it argues it needs to defend itself.
The UN Security Council has held initial consultations on the draft. Israel has so far reacted cautiously.
US Ambassador to the UN John Bolton said the Security Council meeting on Saturday was "very productive".
"We received a lot of encouraging comments on the draft text," he said, adding that member states needed to send it back to their capitals to seek instruction.
Meanwhile the violence has continued, with Israeli commandos clashing with Hezbollah fighters in southern Lebanon.
The Israeli army said eight soldiers had been wounded and several militants were killed in the raid on an apartment in Tyre suspected of housing Hezbollah fighters in the city.
Hezbollah has continued to fire rockets into northern Israel - about 170 were fired on Saturday. Three women were killed in an attack in the mainly Arab village of Arab al-Aramshe.
The draft resolution follows weeks of disagreement over the precise wording of a call to end the violence in Lebanon.
Israel said several militants were killed in its raid in Tyre
Mr Bolton said the text did not include a requirement for an immediate cessation of hostilities.
But it does call for "the immediate cessation by Hezbollah of all attacks and the immediate cessation by Israel of all offensive military actions".
The draft - sent to all 15 member states in the Security Council - also calls for the current UN force in Lebanon to monitor any cessation in fighting.
Lebanon's initial reaction was to express reservations. A Lebanese envoy to the UN, Nouhad Mahmoud, said: "We would have liked to see our concerns more reflected in the text."
He said the text lacked a call for Israeli forces in Lebanon to withdraw. "That is a recipe for more confrontation," he said.
Israeli cabinet minister Isaac Herzog called the text an "important development".
He said military operations would continue "in the coming days, but we have to know that the timetable is becoming increasingly shorter".
Swift passage of the resolution seems likely, says the BBC's James Robbins at the UN in New York, and a formal vote could come as soon as Monday.
Foreign ministers are expected to come to New York for that vote, to give maximum weight to a call to all sides to stop fighting and work for a long-term political settlement, our correspondent adds.
UK Prime Minister Tony Blair welcomed news of the agreement, calling it "an absolutely vital first step in bringing this tragic crisis to an end".
The White House said President George W Bush was "happy with the progress being made".
As the violence on the ground continues, the Israeli army has warned residents in the Lebanese city of Sidon to stay away from rocket launching sites.
In other developments:
- Israeli carried out a commando raid on Tyre, which Hezbollah said it had repelled. Lebanon says one of its soldiers died during the raid
- Hezbollah fired more missiles at the northern Israeli city of Haifa in retaliation, wounding five people
- An Israeli soldier died after coming under Hezbollah mortar fire in the eastern village of Taibeh
- US envoy David Welch held talks in Beirut with Lebanese Prime Minister Fouad Siniora and Lebanese parliament speaker Nabih Berri, the leader of the Shia Amal movement and a possible conduit to Hezbollah
- Thousands marched in London, UK, calling for an immediate ceasefire in Lebanon
Aid agencies have warned of difficulties in delivering supplies to hundreds of thousands of people displaced by the fighting, after four bridges on the main coastal highway north from Beirut were destroyed on Friday.
"Now the main highway is bombed we have a major, major setback... it's like a de facto blockade at the moment," Astrid van Genderen Stort, spokeswoman for the UN refugee agency told the BBC.