On the eve of talks in Washington between the Lebanese and Israeli ambassadors, Lebanese President Joseph Aoun said Beirut would seek an extension of the 10-day, US-mediated ceasefire, which is set to expire on Sunday.
Hostilities between Hezbollah and Israel reignited on March 2, when the Lebanese group opened fire in support of Iran.
The ceasefire in Lebanon emerged separately from Washington's efforts to resolve its conflict with Tehran, though Iran had called for Lebanon to be included in any broader truce. The United States has denied any link between the tracks.
More than 2400 people have been killed in Lebanon since Israel launched an offensive in response to Hezbollah's March 2 attack, according to Lebanese authorities.
Israel has seized a belt of territory at the border where its troops remain, saying it aims to create a buffer zone to shield northern Israel from attacks by Hezbollah, which fired hundreds of rockets at Israel during the conflict.
Lebanon says an Israeli attack on the southern village of Tayri killed two people in a car and targeted rescuers trying to lift a wounded journalist from the rubble.
Israel said it was not preventing rescue teams from operating and had been targeting vehicles leaving a known Hezbollah military structure in the other attack.
Both sides have accused the other of violating the ceasefire agreement.
Aoun said Beirut's envoy to Thursday's talks, Lebanese Ambassador to Washington Nada Moawad, would seek a ceasefire extension and a halt to demolitions being carried out by Israel in villages in the south.
A Lebanese official said Beirut wants a ceasefire extension as a prerequisite for talks to expand beyond the ambassadorial level to the next phase, in which Lebanon would push for an Israeli withdrawal, the return of Lebanese detained in Israel and a delineation of the land border.
Hezbollah, which says the Lebanon ceasefire was the fruit of Iranian pressure, has condemned Beirut for seeking talks with Israel, reflecting wider splits with the government that has sought Hezbollah's peaceful disarmament for a year.
Israeli Foreign Minister Gideon Saar, in a speech, said Israel had taken a "historic decision to negotiate directly with Lebanon after more than 40 years" whilst also calling it a "failed state".
"Let's work together against the terror state that Hezbollah built in your territory," Saar said, addressing Lebanon.
Aoun has cited goals including halting Israeli attacks on Lebanon and securing the withdrawal of Israeli troops. In a speech on Friday, he said a ceasefire should be transformed into "permanent agreements that preserve the rights of our people, the unity of our land, and the sovereignty of our nation".
