Caretaker Prime Minister Najib Mikati has said that “U.S. mediator Amos Hochstein will visit Lebanon soon” and that “the ambiguous files will be resolved face to face.”

U.S. optimism on reaching a Lebanese-Israel ceasefire deal has reached its highest level in a year, a Lebanese government source told Al-Jazeera on Monday.

The European Union “continues to mobilize all the tools at its disposal to support the people affected by the ongoing conflict in Lebanon,” the EU Delegation to Lebanon said.

An Israeli airstrike hit a computer shop in central Beirut's Mar Elias area on Sunday evening, killing two people and wounding 13, the Health Ministry said.

Al-Arabiya television identified the target of the strike as "Hezbollah military commander Mahmoud Madi," saying the computer shop is owned by his brother.

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.

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.

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.

The U.S. ceasefire paper presented to Speaker Nabih Berri consists of 13 points, the most controversial of which is one granting both sides "the right to self-defense," which Lebanon fears could stand for the "freedom of movement" that Israel has demanded and Lebanon has rejected, diplomatic sources in Beirut told Asharq al-Awsat newspaper on Friday.

U.S. Ambassador to Lebanon Lisa Johnson has handed Speaker Nabih Berri a letter containing a ceasefire proposal from U.S. mediator Amos Hochstein and Berri has promised to respond within two to three days, Al-Jadeed TV has reported.

"Berri is optimistic that a ceasefire can be reached within days or a week if no sudden development comes up," Al-Jadeed added.

The U.N. peacekeeping chief whose force monitors Lebanon’s south said redeploying Lebanese troops there is crucial for any solution to more than a year of Hezbollah-Israel clashes that escalated into war in September.

"The redeployment of the Lebanese armed forces is an absolutely central element to any durable settlement," Under Secretary-General for Peace Operations Jean-Pierre Lacroix told reporters during a briefing in the Beirut area.