U.S. mediator Amos Hochstein will visit Beirut on Tuesday and Israel on Wednesday as part of his efforts to push the ceasefire deal forward and amid reported progress in the negotiations, media reports said.

The United Nations Interim Force in Lebanon said on Sunday that a peacekeeping patrol was fired upon "about 40 times" a day earlier, with the culprit "likely from non-state actor members."

The Lebanese army said an Israeli attack on Sunday killed two soldiers, accusing Israel of directly targeting their position in south Lebanon where the Israeli military is fighting Hezbollah.

Hezbollah spokesman Mohammad Afif was killed Sunday in a rare Israeli airstrike targeting the center of the capital Beirut -- outside Hezbollah's traditional strongholds of Dahieh, the south and the Bekaa, a Hezbollah official said.

The strike -- in the Ras al-Nabaa area near Sodeco Square -- targeted a building containing the headquarters of the Lebanese branch of the Baath Party that rules Syria. A Baath member who survived the strike said the building also contained an apartment housing displaced Lebanese.

The Israeli military said about 20 projectiles were identified crossing from Lebanon into Israel on Sunday, with Israeli air defense system intercepting some of them.

Several strikes hit Beirut's southern suburbs Sunday morning and at noon, after the Israeli military warned people to evacuate twice.

Columns of smoke were seen rising over the capital's southern suburbs, where Lebanon's only international airport is located.

Israeli ground forces reached their deepest point in Lebanon since they invaded six weeks ago before pulling back Saturday after battles with Hezbollah militants, Lebanese state media reported.

The clashes and further Israeli bombardment came as Lebanese and Hezbollah officials study a draft proposal presented by the U.S. on ending the war.

Parliament Speaker Nabih Berri has said that the chances of reaching a ceasefire between Lebanon and Israel are now above 50 percent, noting that U.S. mediator Amos Hochstein has obtained a green light from U.S. President-elect Donald Trump to press on with the negotiations.

Three Israeli airstrikes hit the southern suburbs of the Lebanese capital Beirut on Saturday morning, shortly after the Israeli army issued a new call to evacuate the area.

Since Tuesday, Israel has carried out several strikes on the city's southern suburbs, a stronghold of Hezbollah.

Suzanne Karkaba and her father Ali were both civil defense rescuers whose job was to save the injured and recover the dead in Lebanon's war.