Hezbollah is considering a US-Israeli ceasefire proposal, sources told CNN, as diplomatic efforts to end the conflict between Israel and the Lebanese militant group intensify.

Since late September, Israel dramatically escalated its bombardment of Lebanon, vowing to cripple Hezbollah and end its barrages in Israel. More than 3,400 people have been killed in Lebanon by Israeli fire — 80 per cent of them in the past month — Lebanon's Health Ministry says.

Lebanon's caretaker Prime Minister Najib Mikati has appeared to encourage Tehran to convince Hezbollah, which it supports, to agree to a deal that could require the militant group to withdraw from the Israel-Lebanon border.

Israeli officials are insisting on maintaining a capacity to strike Lebanon at any moment as part of conditions to secure a ceasefire with Iran-backed Hezbollah, France's foreign minister said on Wednesday.

Israel carried out more strikes on Hezbollah targets in Lebanon Friday, leveling a building in Beirut. The attack comes as a top Iranian official is vowing to support the Lebanese and the U.S. pushes for a cease-fire.

By Riham Alkousaa and Ari Rabinovitch BEIRUT/JERUSALEM (Reuters) -Diplomacy aimed at securing a ceasefire in Lebanon showed tentative signs of progress on Thursday as Israel pounded its northern neighbour including heavy airstrikes on the stronghold of armed group Hezbollah near Beirut.