Israeli strikes have killed more than 3,000 people in Lebanon since the start of the war between Hezbollah and Israel on March 2, the health ministry said on Monday, after an April 17 ceasefire failed to stop the fighting.

A security agreement that is in the works will include "timetables for disarming all illegal militias, starting with Hezbollah and extending to the smallest Palestinian faction," a Lebanese government source said.

President Joseph Aoun said Monday that he would do the 'impossible' in order to stop the war with Israel, after a ceasefire and direct talks failed to end the fighting.

"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.

Israel has no military solution to the Hezbollah drone threat even if troops occupy all of south Lebanon, Israeli reports said.

A security source told Israel's Kan public broadcaster that a political breakthrough is needed, as occupation will not solve the drones' problem.

Druze leader Walid Jumblat on Monday described the ceasefire between Lebanon and Israel as an "illusion."

Israeli strikes targeted Monday Tebnine, Dweir, Mayfadoun, Majdal Selem, Qana, Deir Ntar, Siddiqine, Maarakeh, Hanaway, Harouf, Kfar Remman, Zawtar, Deir Ames and Deir al-Zahrani in south Lebanon, after a midnight strike on an apartment in Baalbek killed an Islamic Jihad commander and his 17-year-old daughter and wounded two other people.

One person was killed in the strike on a house in Maarakeh, and eight others were wounded.

Hezbollah fired around 200 projectiles at Israel and its troops over the weekend, an Israeli military official said.

"Over the weekend, Hezbollah launched approximately 200 projectiles toward the State of Israel and IDF troops, in a clear and ongoing violation of the ceasefire understandings," the official said, in a statement to AFP.

Speaking at the start of a cabinet meeting on Sunday, Israeli Prime Minister Benjamin Netanyahu said Israel was "holding territory, clearing territory, protecting Israel's communities, but also fighting an enemy that is trying to outsmart us".

"We are facing the challenge of neutralizing FPV (First-Person view) drones," he said, as Hezbollah has increasingly made use of the drones to strike Israeli forces.

Israeli strikes killed seven people in Lebanon on Sunday, including an Islamic Jihad commander, Lebanese authorities and state media said, despite a fragile ceasefire as Hezbollah called U.S.-brokered talks a "dead end".

The health ministry published a "preliminary toll" for Israel's strikes on Sunday, with three people killed in the town of Tayr Felsay, including a child, and two killed in the town of Tayr Debba, including another child.

Lebanon has received a proposal through its embassy in Washington concerning efforts to achieve a complete and comprehensive ceasefire within 24 to 48 hours, starting at midnight between Saturday and Sunday, diplomatic sources said.