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.

Israeli troops have reached their deepest point into Lebanon - before being pushed back by Hezbollah militants.

As a top adviser to Iran's supreme leader Ali Khamenei visited Lebanon for talks, Lebanese officials said a U.S. proposal for a cease-fire deal had been passed on to Hezbollah.