Iran’s supreme leader is said to be pushing Hezbollah towards a ceasefire with Israel as US mediators head to Lebanon to try to broker a deal.

STORY: Lebanon and Hezbollah have agreed to a U.S. proposal for a ceasefire with Israel, a top Lebanese official told Reuters on Monday, as Beirut residents grapple with intensifying Israeli strikes.Ali Hassan Khalil described the effort as the most serious yet to end the fighting.

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.

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.

There are signs of progress on at least one front of the conflict in the Middle East. CBS News senior foreign correspondent Elizabeth Palmer has the latest on reports of a cease-fire deal between Israel and Iran-backed Hezbollah in Lebanon.

A rare Israeli strike in central Beirut killed the Hezbollah militant group's chief spokesman on Sunday, while an Israeli strike in northern Gaza's Beit Lahiya killed at least 30 people, a hospital director there told The Associated Press.

The relentless strikes on Dahieh have visibly weakened Hezbollah’s standing. Israeli officials believe these actions will force the group into submission.