European contingents are thought to be vital if the United Nations is to get an advance party of 3,500 troops on the ground in southern Lebanon by September 2.
The UN Security Council resolution that led to the truce called for 15,000 UN troops to join a similar number of Lebanese army troops already deployed in the south.
European Union countries were due to meet on Wednesday to discuss the rules of engagement for the force.
Italian Prime Minister Romano Prodi on Monday said he had told UN chief Kofi Annan his country was willing to command the force, adding that Mr Annan would make a decision this weekend.
The Lebanese government welcomed Italy's offer of 2,000 troops, the biggest commitment any country has made so far, and Israel has already said it would be happy if Italy led the force.
According to a source close to Mr Prodi, Lebanese Prime Minister Fouad Siniora told his Italian counterpart last night that there was the "unanimous backing" of the Lebanese government for Italy to lead the force.
France had earlier been tipped to take command but sharply cut its anticipated contribution to 200 troops from at least 2,000. Turkey, Spain and other countries are still hesitating.
Italy's right-wing opposition warned the deployment could prove a "kamikaze" mission.
The European jitters have drawn signs of impatience from US President George W Bush, who called for the urgent dispatch of UN peacekeepers to south Lebanon.
"The international community must now designate the leadership of this international force, give it robust rules of engagement and deploy it as quickly as possible to secure the peace," President Bush said in Washington.
During the war, the United States refused to call for an immediate ceasefire, saying political conditions must be put in place to ensure any peace was lasting – which many experts believed was code for the removal of Hezbollah threats to Israel.
At the United Nations, Washington's UN ambassador John Bolton said his country planned a new UN Security Council resolution on disarming Hezbollah, but that this was separate from the quick dispatch of UN troops to Lebanon.
Hezbollah has accepted the deployment of UN and Lebanese troops in its south Lebanese stronghold, but has not promised to leave the area or to dismantle its arsenal of rockets.
Mr Bush also announced a US$230 million (A$302 million) aid package to Lebanon that includes 25,000 tonnes of wheat.
The Lebanese government estimates the damage bill from five weeks of Israeli air strikes has reached US$3.6 billion (A$4.7 billion), and hopes to raise the money at a donor conference in Sweden on August 31.
The World Bank announced it would reallocate US$40 million (A$52.6 million) in previously approved loans for rebuilding efforts in Lebanon and help verify immediate reconstruction needs.
Senior bank official Joseph Saba also said the bank would help Lebanon set up transparent systems to manage international donor funds, and there was no need for a separate trust fund.
"They have asked us to validate the early assessments of requirements for reconstruction and recovery, and of course many of the Lebanese agencies have already begun this work and are far advanced," said Mr Saba, the bank's country director for Lebanon.
He said Beirut had made it clear to donors it wanted to lead its own reconstruction effort.
Despite the truce, Israel's army said its troops shot and hit three gunmen in the south on Monday. It said there was no return fire. Hezbollah said none of its men were killed.
The UN-backed truce has already been jolted by an Israeli commando raid in eastern Lebanon's Bekaa Valley on Saturday, which the United Nations described as a violation.
Meanwhile, the Israeli government has come under further fire at home for its handling of the war, which failed to destroy Hezbollah or secure the release of two kidnapped soldiers.
Israeli reservists published a scathing open letter in which they accused government leaders and top army officers of inept handling of the war.