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Nearly 250 Israeli soldiers have died in south Lebanon since a "security zone" to protect Israel's northern communities from border attacks was established in 1985.
Mr Barak has pledged a pull-out within a year in tandem with resuming peace negotiations with Syria, the powerbroker in Lebanon.
But since his election on Monday he has provided no timetable for action, reaffirming only that he would quickly revive the peace process.
![[ image: width=150]](/olmedia/345000/images/_347931_barak150.jpg)
Mr Barak is also facing the Palestinians' bid for an independent state.
Tayeb Abdel Rahim, a senior aide to Palestinian leader Yasser Arafat, said on Wednesday that a declaration of statehood would come by the end of this year.
Mr Arafat has congratulated Mr Barak on his victory, but some Palestinian officials have already expressed regret at Mr Barak's first comments on the peace process.
Mr Barak has stressed his commitment to a united Jerusalem, but the Palestinians want traditionally Arab east Jerusalem - captured by Israel in the 1967 Middle East war - as their capital.
US President Bill Clinton called Mr Barak on Tuesday to urge a quick launch of negotiations on a final peace settlement with the Palestinians.
The United States has suggested a one-year timeframe for completing the negotiations, which Palestinians hope will yield independence.
On the political front, he is now trying to put together a new coalition government.
Corruption sentence
In the Knesset elections, Mr Barak's Labour Party and its allies - the One Israel coalition - won only 27 of 120 seats.
The BBC Jerusalem correspondent says the question now is whether Mr Barak will try to form a national unity government, which would include the ousted Likud, or stick with Labour's traditional political allies.
It had been suggested that a deal could be forged with the ultra-Orthodox Sephardic Jewish party, Shas, which made significant gains to take its tally of seats from 10 to 17.
But Mr Barak has ruled out any dealings with Shas while its disgraced leader, Aryeh Deri, stays in charge. Mr Deri has resigned from parliament after being sentenced for corruption and fraud.
Mr Barak has 45 days to form a government. In the meantime, outgoing leader Benjamin Netanyahu remains in power as caretaker prime minister.
Palestinian shot
In a separate development, Lebanese security officials say a Palestinian official has been shot dead near the Ain al-Hilweh refugee camp on the outskirts of the city of Sidon.
They said unidentified men opened fire with machine-guns on the official, Amin Kayed, of the Fatah faction of the Palestine Liberation Organisation.
The motive was not immediately known, but correspondents say there have been clashes in the past between rival Palestinian groups for control of the Ain el-Hilweh camp, which is home to tens of thousands of Palestinians.
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