Israel will pursue Hezbollah leaders in Lebanon despite the ceasefire ending the month-long conflict, Prime Minister Ehud Olmert has told parliament.
Roads were jammed as some Lebanese risked returning home
During a stormy session, he defended his conduct of the war saying Hezbollah had been crippled. However the group's leader denied this and claimed victory.
UN Secretary General Kofi Annan said the ceasefire, which came into force early on Monday, seemed to be holding.
Thousands of people are returning to southern Lebanon following the truce.
Fighting ended at 0500 GMT, although Israel said it had killed at least four Hezbollah fighters in later clashes.
Israeli officials told the AFP news agency that in each case soldiers had opened fire "when armed men tried to approach" and had not broken the terms of the UN ceasefire.
Up to 10 rockets were also fired southwards on Monday night and early Tuesday morning but did not cross the Israeli border, the Israeli army said.
No-one was injured and Israel planned no response, military sources added.
In his speech to parliament, Mr Olmert said Hezbollah's "state within a state" and "terror organisation" in southern Lebanon had been destroyed.
However he added that the group's leaders would "not be left alone".
"We will continue pursuing them anywhere, all the time and we do not intend to apologise or ask anyone's permission," he added.
Mr Olmert - who was heckled by some MPs - admitted Israel had made mistakes but took full responsibility for the war.
He advised patience for his critics, who believe the war did not achieve Israel's original goal of dismantling Hezbollah.
The prime minister also said his government would work "with all the means at our disposal" to secure the release of the two soldiers whose capture by Hezbollah sparked the conflict on 12 July.
Lebanese and Israeli military commanders are discussing their fate, an Israeli political source told the BBC.
IMPACT: 34 DAYS OF FIGHTING
About 1,000 - mostly civilians
No precise data on Hezbollah dead
Soldiers: 114 (IDF)
Civilians: 43 (IDF)
700,000 - 900,000 (UNHCR; Lebanese govt)
500,000 (Human Rights Watch)
Hezbollah leader Sheikh Hassan Nasrallah, for his part, said his side had achieved a "strategic, historic victory" against Israel.
He also promised during a videotaped speech on Hezbollah's Al-Manar TV that the group would help Lebanese victims rebuild their homes.
Later on Monday, US President George W Bush blamed Hezbollah and its "state sponsors, Iran and Syria" for the bloodshed in Lebanon.
He said the war had been "part of a broader struggle between freedom and terror".
Mr Bush also vowed to continue to promote democracy in the Middle East. "The freedom agenda will defeat terror," he said.
Mr Annan said the truce appeared to be holding and urged both sides to "continue to consolidate the cessation".
Israel has said its troops will remain in Lebanon until an international peacekeeping force can take control, and that its forces would return fire if attacked.
Roads leading from Beirut and Sidon were jammed with the cars of people returning to inspect their properties and homes.
The BBC's Jim Muir in the town of Bint Jbeil, the site of some of the fiercest fighting, described a scene of devastation with few signs of life.
The body of a woman wrapped in plastic had been left in a shattered building for two weeks, our correspondent added.
The only local residents he found were one man and his disabled wife who had been sheltering in the hospital.
Sweden is to host an international aid conference to raise funds for Lebanon. About 60 governments have been invited to attend the 31 August meeting in Stockholm.
Some 1,000 Lebanese, mostly civilians, and 157 Israelis, 114 of them soldiers, have died in the 34-day conflict.