Aoun's comments came as the Israeli army carried out another series of strikes in south Lebanon, while Hezbollah said it had struck a military target in northern Israel.

Since the start of the ceasefire on April 17, Israel has continued to launch strikes, carry out demolitions and issue evacuation orders in south Lebanon, saying it is targeting the Iran-backed armed group.

On Monday, it issued fresh evacuation warnings to three southern villages, and later repeated its warning to one on the outskirts of the coastal city of Tyre.

Hezbollah has also continued operations against Israeli forces in south Lebanon and northern Israel, including what it said was a drone attack Monday on "the vehicle of the commander of the 300th Brigade of the Israeli enemy army".

On Monday, the health ministry said the death toll from Israeli strikes since the start of the war on March 2 had reached 3,020, with 211 people 18 and under and 116 healthcare workers among those killed.

"The framework that Lebanon has set for the negotiations consists of an Israeli withdrawal, a ceasefire, the deployment of the army along the border, the return of the displaced, and economic aid," Aoun said in a statement Monday.

"My duty, based on my position and my responsibility, is to do the impossible, and to choose what is least costly, in order to stop the war against Lebanon and its people," he added.

Last week the truce was extended for 45 days following a third round of talks between Lebanese and Israeli representatives in Washington, discussions to which Hezbollah is opposed.

But the ceasefire has failed to stop the violence, with Hezbollah on Monday saying it had fired a drone at a military target in northern Israel.

- Ongoing demolitions -

The target was "an Iron Dome platform belonging to the Israeli enemy army" based in a military encampment in northern Israel, Hezbollah said, referring to Israel's air defence system.

The attack was a response to Israeli violations of the ceasefire, it added.

Lebanon's state-run National News Agency reported a series of Israeli strikes across the south.

The Israeli military also issued an evacuation warning for three southern Lebanese towns.

The attacks came a day after Israeli strikes killed seven people in Lebanon, including a member of the group Palestinian Islamic Jihad in the country's northeast, far from the Israel-Lebanon border.

Israeli soldiers have invaded and occupied part of south Lebanon, operating inside an Israeli-declared "yellow line" that runs around 10 kilometres (six miles) north of the border. They have carried out large-scale demolitions in the area.

Israeli Prime Minister Benjamin Netanyahu said on Sunday his country was facing the challenge of neutralising first-person view drones, as Hezbollah has increasingly made use of the tech to strike Israeli forces.

Israeli attacks have killed more than 2,900 people in Lebanon since the start of the war, including more than 400 since the ceasefire took effect on April 17, according to Lebanese authorities.