But underscoring the fragile nature of the truce agreement, the Israeli army said at least four Hezbollah guerrillas had been killed in skirmishes with Israeli soldiers.
A dozen rockets were fired also during the early hours of the ceasefire at positions held by Israeli soldiers in south Lebanon, without causing any injuries, according to the Israeli army.
Israeli soldiers did not return fire at the rocket salvos which violated the ceasefire.
Israel has begun withdrawing some troops but has kept up the pressure with threats to reconquer southern Lebanon and vowed to maintain its air and sea blockade on the country.
Its forces had pursued their battle to wipe out Hezbollah until the last minute, shelling areas in the south and unleashing air strikes on the ancient eastern city of Baalbek, killing five members of the Lebanese army and security forces and two civilians.
Israeli warplanes yesterday dropped leaflets over Beirut blaming Hezbollah and its Iranian and Syrian "masters" for the devastation in Lebanon and warning Israel will respond to any future attack.
"Hezbollah has brought you many achievements: destruction, displacement and death," said one leaflet.
Refugees in Lebanon began streaming towards the south and the first UN aid convoys in days arrived in the war-battered southern city of Tyre.
But aid agencies complained Israel's ban on vehicle movement and an air and sea blockade imposed the day after the war began was still causing problems.
Lebanese Prime Minister Fuoad Siniora called on the five permanent members of the UN Security Council to work to end the blockade.
No apologies for war: Olmert
Israeli Prime Minister Ehud Olmert made no apologies for a war that has killed more than 1,300 people, mostly Lebanese, saying it had changed the face of the Middle East.
"The actions of the Israeli Defence Forces in the air, on the sea and on the ground have brought about a change in the regional strategic balance," said Mr Olmert.
"There is no more state within a state," he said of the Shiite Hezbollah guerrilla movement, which has controlled south Lebanon since Israel withdrew after 22 years of war and occupation in May 2000.
Mr Olmert, facing criticism at home that the massive onslaught failed to deal a knock-out blow to Hezbollah, vowed to hunt down leaders of the militant group.
In other developments, Israel denied a report in the New Yorker magazine that said it had planned its campaign against Hezbollah long before July 12.
The magazine also reported that the US government was closely involved in pre-planning Israel's military operations against Hezbollah, viewing it as a prototype for a US pre-emptive attack to destroy Iran's nuclear installations.
Hezbollah withdrawal 'key'
France's foreign minister has told AFP that the disarmament of Hezbollah militants in Lebanon and their withdrawal to north of the Litani river are indispensable for the Lebanese army and a bolstered international peacekeeping force to deploy in the area.
"The arrangements concerning the deployment of the Lebanese army alongside (the UN force) UNIFIL related to the start of an Israeli withdrawal must necessarily be accompanied first by a withdrawal of Hezbollah north of the Litani," Foreign Minister Philippe Douste-Blazy said.
The move must then be followed by "the implementation of (UN) resolution 1559, namely the disarmament of Hezbollah," he added.
Mr Douste-Blazy made his comments in reaction to an earlier statement by Hezbollah chief Hassan Nasrallah, who said disarmament of his fighters, as demanded by the United Nations, could not be done "in haste".
'Historic victory': Nasrallah
In a televised address, Mr Nasrallah claimed a "historic and strategic victory".
He said the issue of Hezbollah's disarmament could not be resolved "in haste... or by intimidation, pressure or provocation" but through talks among the Lebanese.
Mr Nasrallah also said that beginning today, Hezbollah would begin compensating people whose homes have been destroyed or damaged.
The cessation of hostilities followed a UN resolution aimed at ending the deadliest cross-border conflict in a quarter century, which has claimed the lives of about 1,150 people in Lebanon and 158 Israelis.
Hezbollah 'suffered defeat': Bush
US President George W. Bush said that Hezbollah had "suffered a defeat" in its conflict with Israel and predicted the group's influence in Lebanon would decline.
"Hezbollah started the crisis. And Hezbollah suffered a defeat in this crisis," Mr Bush said at the US State Department, pointing to the planned deployment of a multinational force in southern Lebanon to prevent the militia from striking Israel.
The White House, which has staunchly supported Israel throughout the fighting, expressed cautious optimism about the ceasefire and said Hezbollah had been weakened.
"We hope that everybody will stay true to the ceasefire and that the government of Lebanon, again, will be able to have credibility," spokesman Tony Snow told reporters.
The US State Department said the UN resolution to halt the fighting, if successful, will mark a "strategic setback" for Iran and Syria, considered the main backers of Hezbollah.
Annan 'relieved'
UN Secretary General Kofi Annan said he was "relieved" the cessation of hostilities appeared to be holding, and urged UN member states to contribute troops to a UN force there.
The conflict began on July 12 after Hezbollah guerrillas captured two Israeli servicemen in a cross border raid, just weeks after a similar attack by Palestinian militants triggered a massive offensive against the Gaza Strip.
During the 34-day conflict, Hezbollah militants engaged in fierce ground battles with Israeli soldiers and fired around 4,000 rockets into Israel, killing 41 civilians and 117 soldiers, according to AFP.
More than 900,000 people were displaced by Israeli bombardments that also destroyed thousands of homes, dozens of bridges and hundreds of kilometres of roads.
Yesterday’s ceasefire came a day after some of the most intense fighting of the conflict, with at least 38 Lebanese civilians and four soldiers killed and nine Israeli soldiers and a civilian killed as the militia fired a record 250 rockets at the Jewish state, AFP reported.
Ceasefire timing
The timing for the ceasefire was unveiled by Mr Annan on Saturday following the adoption of UN Security Council Resolution 1701 calling for a cessation of hostilities and deployment of an international force in south Lebanon.
Israel and Lebanon both endorsed the resolution, while Mr Nasrallah said his fighters would abide by any ceasefire, but would also fight on until the last Israeli soldier left Lebanon.
Israel has urged the world to apply UN resolution 1701 firmly, warning that Hezbollah must be dismantled and the Lebanese army quickly deployed in the militia's stronghold in the south.
The commander of UN forces in Lebanon met yesterday with Lebanese and Israeli army officers to discuss the withdrawal of Israeli forces and the Lebanese army deployment in south Lebanon.