Meanwhile, Arab foreign ministers held an emergency meeting in the war-ravaged capital of Beirut on Monday to discuss the crisis, amid warnings the conflict could escalate into the region.
The council was to hold new consultations on a French-US draft after Lebanon opposed the text because it does not order an immediate withdrawal of Israeli troops from Lebanese territory once hostilities end.
Following the Lebanese objections, the council's five permanent members could not say when a vote on a text would be carried out.
"I don't think that there is a magic wand" to settle problems over the resolution, said Russia's UN Ambassador Vitaly Churkin, who urged Lebanon and the Arab world to give the proposed resolution "a serious reading".
"And I think if they do, they'll see that there is much in it which is very much in the interests of Lebanon," he told reporters after discussing the new holdup with envoys from France, the United States, Britain and China.
The impatience has also been hinted at by US Secretary of State Condoleezza Rice and France.
"I just want to say, let's vote the resolution and then there's going to be an obligation by Lebanon and by Israel to obey that resolution," she told ABC television.
"No one wants to see Israel permanently in Lebanon. Nobody wants to do that. The Israelis don't want it, the Lebanese don't want it, so I think there is a basis here for moving forward," Rice said.
French President Jacques Chirac said of the deadlock: "Everyone should accept their responsibilities."
He added in a statement: "Our aim is to arrive as soon as possible at a sustainable ceasefire through a political agreement which takes into account the worries of all the parties."
The current text does not call for an Israeli withdrawal, only for "full respect for the Blue Line", the unofficial border between Lebanon and Israel.
Lebanon also wants the text to state that within 72 hours of a truce, the UN Interim Force (UNIFIL) in Lebanon would hand over a buffer zone on the frontier to the Lebanese army.
Lebanon's UN representative Nouhad Mahmoud said the Beirut government wants any international force to play more of a support role to the Lebanese armed forces as they seek to take control of the south of the country where Hezbollah is now dominant.
Rice has also warned that even if the first resolution is passed it will not halt all fighting. More than three weeks of conflict has killed more than 1,000 people, mostly civilians, in Lebanon and Israel.
"I would hope that you would see, very early on, an end to the kind of large-scale violence, large-scale military operations," Rice said.
"But I can't say that you should rule out that there could be skirmishes of some kind for some time to come."
"We're trying to deal with a problem that has been festering and brewing in Lebanon now for years and years and years, and so it's not going to be solved by one resolution in the Security Council," Rice declared.
The United States and France have embarked on intensive contacts with Lebanon and Israel to accept the draft. Israel, which has pursued its military operation, has not publicly stated whether is accepts or rejects the proposed resolution.
The Israeli Ambassador to Washington, Daniel Ayalon, said Sunday that his country's army will carry on fighting Hezbollah in Lebanon until two soldiers, whose capture sparked the conflict last month, are returned.
Ambassador Ayalon said Israel would cease fire once a UN Security Council resolution aimed at ending the conflict was passed -- but only if the measure was imposed on both sides.