Smoke billows from fires ignited by Israeli shelling on the forested areas of the southern Lebanese village of Deir Mimas. AFP

A US envoy held talks with top Israeli leaders to press for de-escalation on the Lebanese border, as an Israeli official said Hezbollah had fired thousands of projectiles towards Israel since the start of the Gaza war.

Israel and Hezbollah, a Hamas ally, have traded near-daily cross-border fire since the Palestinian group's October 7 attack on Israel which triggered war in the Gaza Strip.

But exchanges have escalated and last week saw Hezbollah's largest simultaneous attack, after an Israeli strike killed a senior commander from the group.

United States presidential special envoy Amos Hochstein met with Israeli Prime Minister Benjamin Netanyahu and his team in Jerusalem days after Secretary of State Antony Blinken said on a Middle East tour that a Gaza ceasefire was the best way to resolve the Hezbollah-Israel violence.

"I can confirm that (US President Joe) Biden's envoy... met with our prime minister," Israeli government spokesman David Mencer told a press briefing.

Mencer also said Hezbollah has fired more than 5,000 rockets, anti-tank missiles and explosive drones at Israeli territory since hostilities started.

Israeli men check a crater on the ground that was hit by a Hezbollah rocket near the Lebanon border. AFP

"We are defending against Hezbollah aggression. There is no territorial dispute between Lebanon and Israel," Mencer said.

Hochstein also met with Israeli President Isaac Herzog, with whom he discussed "the relentless attacks and rocket fire from Hezbollah, instigated by Iran, towards Israel's northern towns and cities," according to a statement from the presidential office.

Hezbollah last week said it has carried out more than 2,100 military operations against Israel since October 8, the day after Hamas's attack.

Hezbollah escalated attacks last week after a commander, Taleb Abdallah, was killed in an Israeli strike in the village of Jouaiyya. The Israeli army described him as "one of Hezbollah's most senior commanders in southern Lebanon".

The Iran-backed Lebanese movement said it launched rocket and missile barrages as well as "attack drones" against Isreali military positions in response.

An Israeli soldier checks a house that was hit by a Hezbollah rocket near the Lebanon border. AFP

On Monday, the Israeli military announced it had killed Mohammad Mustafa Ayoub, describing him as a key Hezbollah operative from the group's rocket and missile department in the Selaa area of southern Lebanon.

Hezbollah confirmed the death of the fighter from its elite Radwan unit.

Israeli military spokesman Rear Admiral Daniel Hagari on Sunday warned that "Hezbollah's increasing aggression is bringing us to the brink of what could be a wider escalation -- one that could have devastating consequences for Lebanon and the entire region."

The United Nations has expressed concern about the recent escalation on the Israel-Lebanon border and warned of the danger of miscalculation causing a wider conflict.

Agence France-Presse