US Secretary of State Condoleezza Rice says she hopes to see a vote in a day or two on a UN draft resolution aimed at ending fighting between Israel and Hezbollah militants.
She said the resolution is an important first step to ending large-scale attacks, adding she expects some skirmishes will continue.
The UN Security Council was to meet on Sunday to discuss the draft which calls for an immediate end to Hezbollah attacks on Israel and a stop to offensive military operations by Israel.
It also urges the "disarmament of all armed groups in Lebanon."
On a visit to Beirut, Syria's Foreign Minister Walid Moallem rejected the UN resolution as what he called a "recipe for the continuation of war."
White House National Security Adviser Stephen Hadley says officials hope a separate U.N. measure on deploying international forces to southern Lebanon will come in "days, not weeks."
Lebanese officials have criticized the draft for failing to require Israel to withdraw its forces from Lebanon.
Iranian state media reports that President Mahmoud Ahmadinejad phoned his Syrian counterpart Bashar al-Assad to discuss mediation efforts.
In Damascus, Mr. Assad also held talks with Arab League Secretary-General Amr Moussa about ways to end fighting.