Top Lebanese official says written response has been delivered to the US, describing it as the most serious effort yet to secure a truce

Netanyahu also said there was no evidence Hezbollah would respect a cease-fire.

A top Iranian official has pledged his country's unwavering support for Lebanon after talks with Lebanese leaders on the Israel-Hezbollah war.

A senior U.S. official said on Tuesday there was a "real opportunity" to end the conflict between Israel and Hezbollah and that gaps were narrowing, signalling progress in Washington's efforts to clinch a ceasefire agreement.

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.

BEIRUT − Lebanon and the militant group Hezbollah have agreed to a U.S. ceasefire proposal and made some comments on the content, a top Lebanese official told Reuters on Monday, describing the effort as the most serious yet to end weeks of fighting and Israeli bombardments.

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.

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.