As intensive talks continued in New York, UN Secretary General Kofi Annan spoke with the French and US presidents, Jacques Chirac and George W. Bush.
Mr Chirac told Mr Annan that France was looking for "wording acceptable to all" in a resolution being formulated to call for a halt to violence between Israel and Hezbollah, Mr Chirac's office said.
Mr Bush and Mr Annan discussed the diplomatic negotiations and "efforts to create a way forward," White House spokesman Tony Snow said.
Mr Bush also "expressed his concern about continued violence in Lebanon and Israel," Mr Snow said.
Asked whether this meant that there had been a breakthrough in talks to craft a resolution, Mr Snow said: "No, I don't think so."
US Secretary of State Condoleezza Rice said in an interview with MSNBC television that the UN resolution could be passed “within days”.
"We are moving, I think pretty effectively now with the French and with others in the United Nations toward a cessation of hostilities," Ms Rice said.
A first step would be to lay down a political framework to prevent a return to violence, which the United States has previously said would involve bolstering the Lebanese government to help it disarm Hezbollah, Ms Rice said.
"We then have to move to a second phase, to a security force and we do have to get to a sustainable and permanent ceasefire.
"This is a process that we will be beginning with the resolution that we hope will be ready and I believe will be ready within days," she added.
Mr Annan had also spoken by telephone to British Prime Minister Tony Blair, Lebanese Prime Minister Fuad Siniora and Russia's acting foreign minister Andrei Denisov, the UN said.
Mr Annan was "deeply, deeply concerned that it is taking so long" to pass a resolution, a spokesman said earlier.
Amid mounting international frustration over the pace of negotiations, the French and US delegations at the UN imposed a news blackout on the talks.
There was no indication when the full UN Security Council might vote on a resolution, though the council's president said the body was ready to meet at any moment.
US ambassador to the UN, John Bolton, and his French counterpart Jean-Marc de La Sabliere met until late on Thursday and held more negotiations on Friday in a bid to agree the wording of a resolution, diplomats said.
The two sides "are trying to work out a solution" and their differences are narrowing, said one diplomat on condition of anonymity.
But he added that the two sides are expected to keep working through the weekend.
France has proposed a resolution calling for a "cessation of hostilities."
US officials say they would rather use a more vague term to describe the fighting.
A second sticking point is over the organisation of an international force for Lebanon and what would happen to Israeli troops in southern Lebanon.
Another diplomat said that the two ambassadors were still using a text proposed by France as a basis for the negotiation. "The Americans are suggesting amendments," the diplomat told news agency AFP.
Other nations, particularly in the Islamic world, are impatient to see the UN Security Council make an urgent call to end the fighting that has left more than 900 dead in Lebanon and Israel since July 12.
Russia's UN ambassador Vitaly Churkin said: "We need an urgent ceasefire, that is all I can tell you."
Neither Mr Bolton nor Mr de La Sabliere attended a briefing to the Security Council on the growing humanitarian crisis in Lebanon.
France's draft resolution calls for an "immediate cessation of hostilities" -- a term which could be changed -- and once a political agreement is in place for the sending of an international force to south Lebanon.
It also demands "full respect" of the Blue Line, the unofficial frontier between Israel and Lebanon, by both sides.
It calls for the disarming of Hezbollah and the release of two Israeli soldiers abducted by the militia -- the act which sparked Israel's military offensive.
The text also calls for "the settlement" of a dispute over Lebanese prisoners held by Israel.
The UN Security Council is in "standby mode," according to Ghanaian envoy Nana Effah-Apenteng, the council president for August who organises its agenda.
"If it happens tomorrow, we will meet. If it happens Sunday we will meet."