A senior Israeli official and Lebanese Foreign Minister Abdallah Bou Habib appeared optimistic that a deal could be reached, cooling a second front for Israel's military that is also battling the Palestinian militant group Hamas in Gaza.

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

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

At a conference in Rome, Lebanese Foreign Minister Abdallah Bou Habib expressed hope that a deal to end the deadliest spillover from the Gaza war could be sealed by Tuesday night.

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.

Bou Habib said the Lebanese army would be ready to have at least 5,000 troops deployed in southern Lebanon as Israeli troops withdraw, and that the United States could play a role in rebuilding infrastructure destroyed by Israeli strikes.

Israel demands effective UN enforcement of an eventual ceasefire with Lebanon and will show "zero tolerance" toward any infraction, Defence Minister Israel Katz said on Tuesday.

The agreement with Lebanon will maintain Israel's freedom of operation there to act in defence to remove threats posed by Hezbollah and enable displaced residents to return safely to their homes in northern Israel, Israeli government spokesperson David Mencer told Reuters.

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 UN rights chief voiced concern about the escalation of hostilities in Lebanon, where his office said nearly 100 people had been reported killed by Israeli airstrikes in recent days, including women, children and medics.

Israel says it targets military capabilities in Lebanon and Gaza and takes steps to mitigate the risk of harm to civilians. It accuses Hezbollah, like Hamas in Gaza, of hiding among civilians, which they deny.