Israel looks set to approve a U.S. plan for a ceasefire with Lebanon's Hezbollah on Tuesday, a senior Israeli official said, clearing the way for an end to the conflict that has killed thousands of people since it was ignited by the Gaza war 14 months ago.

That optimism was shared by Lebanese Foreign Minister Abdallah Bou Habib who expressed hope at a G7 meeting in Italy that a ceasefire would be reached by Tuesday night.

Israel's security cabinet is expected to convene later on Tuesday to discuss and likely approve the text at a meeting chaired by Prime Minister Benjamin Netanyahu, the official said.

This would pave the way for a ceasefire declaration by U.S. President Joe Biden and French President Emmanuel Macron, four senior Lebanese sources told Reuters on Monday.

In Washington, White House national security spokesperson John Kirby said on Monday, "We're close" but "nothing is done until everything is done". The French presidency said discussions on a ceasefire between Israel and the Iran-backed Hezbollah had made significant progress.

The agreement requires Israeli troops to withdraw from south Lebanon and Lebanon's army to deploy in the region - a Hezbollah stronghold - within 60 days, officials say. Hezbollah would end its armed presence along the border south of the Litani River.

The proposal has already won approval in Beirut, where Lebanon's deputy parliament speaker Elias Bou Saab told Reuters on Monday there were no serious obstacles left to start implementing it - unless Netanyahu changed his mind.

Signs of a diplomatic breakthrough have been accompanied by a military escalation. Israeli airstrikes on Tuesday demolished more of Beirut's Hezbollah-controlled southern suburbs, while the armed group has kept up rocket fire into Israel.

The widespread destruction left by Israeli airstrikes has brought into focus a huge reconstruction bill awaiting cash-strapped Lebanon, with more than 1 million people displaced and many left homeless heading into winter.

In Israel, a ceasefire will pave the way for 60,000 people to return to homes in the north, which they evacuated as Hezbollah began firing rockets in support of its Palestinian ally Hamas a day after that group's Oct. 7, 2023 assault.

'The missiles are chasing us'

Israel has dealt Hezbollah massive blows since going on the offensive against the group in September, killing its leader Sayyed Hassan Nasrallah and other top commanders, and pounding areas of Lebanon where the group holds sway.

"Regarding the ceasefire, I think it will be implemented. Both sides are tired - both sides are tired," said Selim Ayoub, a 37-year-old mechanic from Beirut's southern suburbs.

Hezbollah launched some 250 rockets on Sunday in one of its heaviest barrages yet. The northern Israeli city of Nahariya came under more rocket fire overnight.

"As we were about to sleep, we suddenly heard a huge explosion, the window in our fortified room was shaking," said Ofir Ben David, who was evacuated earlier in the conflict from the Israeli community of Shomera on the Lebanese border.

"The missiles are chasing us all the time."

Diplomacy to end the fighting has focused on restoring a ceasefire based on U.N. Security Council Resolution 1701, which ended the last major war between Hezbollah and Israel in 2006.

Israel's ambassador to the United Nations, Danny Danon, said on Monday that Israel would maintain an ability to strike southern Lebanon under any agreement.

Lebanon has previously objected to Israel being granted such a right, and Lebanese officials have said such language is not included in the draft proposal.

Two Israeli officials told Reuters that Israel has a side agreement with the U.S. allowing it to take action in Lebanon against "imminent threats."

Senior Hezbollah official Mohammad Raad, writing in a Lebanese newspaper on Tuesday, said it was unlikely Israel would "accept any talk about halting its aggression against Lebanon without pressure or without exhausting the option of using force on the ground".

"However, we will wait and see the results of the indirect negotiations," he wrote.

Hezbollah, seen as a terrorist group by Washington, has endorsed its ally Parliament Speaker Nabih Berri to negotiate.

Death toll

Over the past year, more than 3,750 people have been killed in Lebanon and over one million have been forced from their homes, according to Lebanon's health ministry, which does not distinguish between civilians and combatants in its figures.

Hezbollah strikes have killed 45 civilians in northern Israel and the Israeli-occupied Golan Heights. At least 73 Israeli soldiers have been killed in northern Israel, the Golan Heights and in combat in southern Lebanon, according to Israeli authorities.

Biden's administration, which leaves office in January, has emphasised diplomacy to end the Lebanon conflict, even as all negotiations to halt the parallel war in Gaza are frozen.

U.S. Middle East envoy Brett McGurk will be in Saudi Arabia on Tuesday to discuss using a potential Lebanon ceasefire as a catalyst for a deal to end hostilities in Gaza, the White House said.