US envoy Amos Hochstein Tuesday called for the "urgent" de-escalation of cross-border exchanges of fire between Lebanon's Hezbollah and Israeli forces raging since the start of the Gaza war.

"The conflict... between Israel and Hezbollah has gone on for long enough," the presidential envoy said on a visit to Beirut.

"It's in everyone's interest to resolve it quickly and diplomatically -- that is both achievable and it is urgent."

The powerful Iran-backed armed group, an ally of the Palestinian militant movement Hamas, stepped up attacks on northern Israel last week after an Israeli strike killed one of its senior commanders.

But since Saturday afternoon, Hezbollah has not claimed any attacks against Israel, despite Israeli strikes on the border area in Lebanon's south including one on Monday that killed a fighter.

Hochstein met with Lebanese parliament speaker Nabih Berri, a day after holding talks in Jerusalem with Israeli Prime Minister Benjamin Netanyahu.

"Speaker Berri and I had a very a good discussion," Hochstein said.

"We discussed the current security and political situation in Lebanon as well as the deal on the table right now with respect to Gaza, which also presents an opportunity to end the conflict across the Blue Line", the demarcation line between Israel and Lebanon.

US President Joe Biden last month outlined a truce proposal which Hochstein said would "ultimately the end of the conflict in Gaza".

"A ceasefire in Gaza and, or, an alternative diplomatic solution could also bring the conflict across the Blue Line to an end" and allow the return of displaced civilians to southern Lebanon and northern Israel, the envoy added.

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 that sparked the ongoing war in the Gaza Strip.

The Israel-Lebanon border violence has killed at least 473 people on the Lebanese side, most of them fighters but also including 92 civilians, according to an AFP tally.

Israeli authorities say at least 15 soldiers and 11 civilians have been killed in the country's north.