A US envoy was in Israel to press for deescalation with Lebanon, as an Israeli official said Hezbollah had fired more than 5,000 projectiles across the border since the start of the Gaza war.

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

US 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.

It came as Mencer said Hezbollah has fired over 5,000 rockets, anti-tank missiles and explosive UAVs at Israeli territory since hostilities started.

"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 says it has carried out more than 2,100 military operations against Israel since October 8, the day after Hamas's attack, according to a statement released by the militant group last week.

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

That prompted the Iran-backed Lebanese movement to launch targeted strikes on several Israeli army bases, it said.

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 escalation.