Israel's security cabinet was set to discuss a proposed ceasefire in its war with Hezbollah in Lebanon on Tuesday afternoon, a senior official said, after the White House voiced optimism that a deal was close.

The United States, European Union and United Nations have pushed for a halt to the long-running hostilities between Israel and Hezbollah, which escalated into full-scale war in late September.

As truce talks intensified, exchanges of cross-border fire between Israel and the Iran-backed Hezbollah have also increased, with Israel reporting around 250 projectiles launched at its territory on Sunday alone.

On Tuesday, strikes hit Hezbollah's south Beirut stronghold shortly after the Israeli military called for people to evacuate. 

AFPTV footage showed multiple plumes of smoke rising from the area, a day after the Lebanese health ministry said Israeli air strikes killed 31 people, mostly in southern Lebanon.

On the diplomatic front, Israeli Deputy Foreign Minister Sharren Haskel said on Tuesday that the security cabinet would meet later in the day to discuss a ceasefire deal, though she declined "to go into details about it because of the sensitivity of the issue".

An Israeli official speaking on condition of anonymity had previously said the security cabinet would make its decision on Tuesday evening.

US National Security Council spokesman John Kirby said on Monday that the talks were progressing but not yet finalized, though they had reached a "point where we're close".

The United States and France have led the efforts to broker a ceasefire.

US news outlet Axios reported that the draft agreement included a 60-day transition period.

During that time, Israeli forces would withdraw, the Lebanese army would redeploy near the border and Hezbollah would move its heavy weapons north of the Litani River, Axios said.

A US-led committee would oversee implementation, with provisions allowing Israel to act against imminent threats if Lebanese forces failed to intervene.

Israeli Defense Minister Israel Katz told the UN's Lebanon envoy on Tuesday that his country would have "zero tolerance" when defending its security interests, even after a truce.

"If you do not act, we will do it, forcefully," Katz told envoy Janine Hennis-Plasschaert during a meeting in Tel Aviv, according to a statement from his office.

Deal a 'mistake'

Israeli media have reported that Prime Minister Benjamin Netanyahu is likely to endorse the US ceasefire proposal.

The war in Lebanon followed nearly a year of limited cross-border exchanges of fire initiated by Hezbollah. The Lebanese group said it was acting in support of Hamas after the Palestinian group's October 7, 2023 attack on Israel, which sparked the war in Gaza.

Lebanon says at least 3,768 people have been killed in the country since October 2023, most of them in the past several weeks.

On the Israeli side, the Lebanon hostilities have killed at least 82 soldiers and 47 civilians, authorities say.

The initial exchanges of fire forced tens of thousands of Israelis to flee their homes, and Israeli officials have said they are fighting so the residents can return safely.

Some northern residents questioned whether that would be possible under a ceasefire.

"In my opinion, it would be a serious mistake to sign an agreement as long as Hezbollah has not been completely eliminated," said Maryam Younnes, 29, a student from Maalot-Tarshiha.

Israel's far-right National Security Minister Itamar Ben Gvir warned on X that reaching a Lebanon ceasefire deal would be a "historic missed opportunity to eradicate Hezbollah".

But EU foreign policy chief Josep Borrell said Israel had "no more excuses" to refuse a deal.

'Scavenging among the rubble'

Sustained efforts this year by mediators to secure a truce and hostage-release deal in the Gaza war have failed.

Qatar early this month said it was suspending its mediation role until the warring sides showed "seriousness".

In Gaza, the civil defense agency said on Tuesday that 11 people were killed in nighttime Israeli strikes across the Palestinian territory.

With the violence showing no signs of stopping, Gazans were left "scavenging among the rubble" for food, said Louise Wateridge, spokeswoman for the UN agency for Palestinian refugees, UNRWA.

Such conditions put people at risk of encountering unexploded and unused ordnance that can be found in many populated areas of the territory, the Danish Refugee Council said.

Hamas's October 7 attack on Israel last year resulted in the deaths of 1,207 people, most of them civilians, according to an AFP tally of Israeli official figures.

That toll includes an Israeli soldier who was wounded during Hamas's attack and died on Tuesday from his injuries more than a year later, the military said.

Israel's retaliatory campaign has killed 44,249 people in Gaza, according to figures from the Hamas-run territory's health ministry that the United Nations considers reliable.

by Marc Jourdier with Layal Abou Rahal in Beirut