On Monday, the Lebanese health ministry said the death toll from Israeli strikes since the start of the war had reached 3,020, with 211 people 18 and under and 116 healthcare workers among those killed.
Lebanese President Joseph Aoun said Monday he was ready to "do the impossible" to stop the war with Israel, as strikes continued to batter the country despite a ceasefire.
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.
While a ceasefire was announced on 17 April, it has failed to stop the violence between Israel and Hezbollah, which have continued to launch strikes as they accuse each other of violating the agreement.
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 not a party, and is opposed to.
"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.
Ceasefire fails to stop violence
Hezbollah said it had fired a drone targeting "an Iron Dome platform belonging to the Israeli enemy army" based in a military encampment in northern Israel.
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.
Israel has also continued to carry out demolitions and issue evacuation orders in villages along Lebanon's southern border.
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.
Israeli soldiers have invaded and occupied part of south Lebanon, operating inside an Israeli-declared "yellow line" that runs around 10 kilometres north of the border. They have carried out large-scale demolitions in the area, but claim they have no territorial ambitions there.
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.
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.