The truce between Israel and Hezbollah remains intact despite sporadic violence in southern Lebanon.
Thousands of displaced Lebanese are returning to their homes
Israel's army said Hezbollah militants fired several mortars overnight but it did not respond as none landed over the border and no-one was injured.
Both sides have claimed they were successful in the conflict.
As thousands of Lebanese people return home after the fighting, the presidents of US and Iran have blamed each other for fuelling the crisis.
US President George W Bush accused Iran of backing armed groups in Lebanon and Iraq "in the hope of stopping democracy from taking hold".
Iran's President Mahmoud Ahmadinejad blamed Washington for providing Israel with weapons which he said had been used to target women and children in Lebanon.
Syrian President Bashar al-Assad said the US plan for a "new Middle East" had collapsed after Hezbollah's success in fighting Israel.
Overnight, Israeli troops left the southern Christian town of Marjayoun, Lebanese security sources said.
Israeli military sources say that between five and 10 mortars were fired southwards on Monday night and early on Tuesday morning.
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)
The Israeli military has said repeatedly it wants the ceasefire to succeed and is playing down this incident, says the BBC's Rob Norris in Jerusalem.
Earlier, Israeli troops clashed with Hezbollah fighters several times across southern Lebanon, killing at least one guerrilla.
Hezbollah has always maintained it will attack any Israeli forces in Lebanon even though it has also said that it will abide by the terms of the ceasefire.
The head of the United Nations peacekeeping force in Lebanon, Gen Alain Pellegrini, warned any provocation could quickly escalate into a major confrontation between Israel and Hezbollah.
He appealed for international reinforcements to be sent as soon as possible to prevent the ceasefire from unravelling.
Lebanon's Defence Minister Elias Murr said that by the end of the week, the Lebanese army would deploy 15,000 troops on the boundaries of the southern Litani River, some 30km (19 miles) from the border with Israel.
In the meantime, international troops currently in Lebanon would assume positions vacated by the Israeli army before handing them over to the Lebanese troops.
Mr Murr said the army would not disarm Hezbollah, but added he expected the group to co-operate, adding there would be no arms in southern Lebanon other than those of Lebanese forces once they deployed.
Hezbollah's leader Sheikh Hassan Nasrallah has claimed an historic victory, in an address broadcast on the group's television channel.
It was the wrong time, he added, for any discussion about disarming the movement - as laid down in the recent UN resolution.
He also said Hezbollah would start giving money from Tuesday to internally displaced people to cover one year's rent while they waited for their houses to be rebuilt.
Israeli Prime Minister Ehud Olmert defended his leadership in an address to parliament on Monday, saying Hezbollah had been dealt a harsh blow.
He said there had been shortcomings in the conduct of the war, but insisted it had changed the region's strategic balance - ending what he called Hezbollah's state-within-a-state in southern Lebanon.
But his critics are angry that Israel has failed to crush Hezbollah as Mr Olmert had promised at the start of the campaign, our correspondent says.
They doubt the group will ever give up its weapons and they worry that even if Hezbollah withdraws from southern Lebanon, it may still be able to fire long-range rockets from elsewhere.
Most of all, they are furious that the two Israeli soldiers whose capture by Hezbollah sparked the crisis still have not been released.
In an opinion poll of 500 Israelis by a leading Hebrew financial paper published on Monday night, more than half said the army had not achieved its aims in Lebanon.