Israel-Gaza-Lebanon live updates: American hostage's father makes plea to Biden and Trump

The Israel Defense Forces said Tuesday that its forces conducted operations near Lebanon's Litani River -- the waterway around 18 miles of the Israeli border which Israeli leaders have demanded serve as a buffer keeping Hezbollah units out of the country's south.

Reaching the Litani would mark the deepest penetration of Israeli forces into Lebanon since the IDF withdrew from the country in 2000. Israeli troops did not push up to the Litani in the 2006 war with Hezbollah.

Soldiers "raided several terrorist targets, engaged in close-quarters combat with terrorists, located and destroyed dozens of launchers, thousands of rockets and missiles and weapons storage facilities" in operations in the Litani River region, the IDF said in a post to X.

-ABC News' Jordana Miller

Lebanon's Ministry of Public Health said Tuesday that the death toll from Israel's military operations in the country had risen to 3,768 people as of Sunday.

Another 15,699 people have been wounded since renewed fighting between the Israel Defense Forces and Hezbollah began on Oct. 8, 2023, the ministry said.

Israel continued airstrikes on Monday night and Tuesday morning even amid reports of an imminent cease-fire deal. Lebanon's National News Agency reported six people killed in multiple attacks in the southern Nabatieh Governorate.

IDF spokesperson Avichay Adraee also issued fresh evacuation warnings for Beirut's southern Dahiya area on Tuesday morning ahead of planned airstrikes there.

-ABC News' Ghazi Balkiz

A cease-fire between Israel and Hezbollah would begin soon after its announcement, with the aim of achieving a permanent cease-fire after 60 days, according to an Israeli source with knowledge of the potential deal.

The U.S. will head a committee, joined by French and Arab partners, to monitor and verify the implementation of the ceasefire, the source said.

Prime Minister Benjamin Netanyahu will hold a security cabinet meeting Tuesday to discuss the deal and hold a cabinet vote, Israeli officials said.

There is almost unanimous support in the cabinet for the U.S.-brokered cease-fire deal, and it is expected to be approved. Far-right leader Ben Gvir is expected to vote against it.

-ABC News' Jordana Miller

The U.S. is hopeful that Israel and Hezbollah are close to a cease-fire deal, but striking a pact "is up to the parties, not to us," State Department spokesperson Matthew Miller said in a briefing Monday.

"We don't believe we have an agreement yet. We believe we're close to an agreement. We believe that we have narrowed the gap significantly, but there are still steps that we need to see taken, but we hope -- we hope that we can get there," Miller said.

Echoing comments earlier Monday by White House National Security spokesperson John Kirby, Miller emphasized that "nothing's final until everything's final."

"Oftentimes the very last stages of an agreement are the most difficult, because the hardest issues are left to the end," Miller said.

-ABC News' Chris Boccia