Israel's military chief of staff Lieutenant General Eyal Zamir issued a sharp warning to troops about looting on Monday, and said using social media to spread "questionable" messages was crossing "a red line".

Israeli Prime Minister Benjamin Netanyahu on Monday said rockets and drones possessed by Hezbollah remained a key threat that demanded further military action by Israel's military in Lebanon.

Israeli Defense Minister Israel Katz warned Monday that Hezbollah's defiance would bring catastrophic consequences for Lebanon after the group's leader Naim Qassem rejected proposed direct talks between Lebanon and Israel.

President Joseph Aoun spent all of Sunday holding contacts with officials in Washington to follow up on the situation on the ground in the south and to curb military escalation, a media report said on Monday.

Extensive consultations will begin in Beirut among President Joseph Aoun, Speaker Nabih Berri and PM Nawaf Salam, and also with the political forces, to "pave the way for decisions described as pivotal that Lebanon must make regarding the negotiation process between Lebanon and Israel," a media report said on Monday.

"While awaiting the crystallization of the next steps, the broad outlines of which were established during the second round of talks between the Lebanese and Israeli ambassadors at the White House, culminating in a meeting with U.S. President Donald Trump, it was reported that a new U.S. memorandum will be issued by the State Department outlining renewed instructions for the ceasefire," An-Nahar newspaper reported.

The Israeli army has begun reducing its forces in Lebanon and the remaining forces continue their operations on the border within the framework of the ceasefire restrictions, Israel's Maariv newspaper reported.

Lebanese Forces leader Samir Geagea said Hezbollah is incapable of reaching a deal to end the war, urging the group to let the government do its job.

Geagea told al-Jadeed on Sunday evening that President Joseph Aoun and Prime Minister Nawaf Salam are doing "what must be done" to get Lebanon out of the predicament into which it was dragged.

The United Nations' UNIFIL peacekeeping force said it held a memorial in Beirut for an Indonesian peacekeeper who died on Friday after being wounded in a blast in south Lebanon last month.

A preliminary U.N. investigation found that an Israeli tank shell caused the explosion.

Hezbollah has rejected Israeli Prime Minister Benjamin Netanyahu's accusation that it was jeopardizing a ceasefire and said it would keep responding to Israel's own violations and occupation of south Lebanon.

In a statement Sunday, Hezbollah said its attacks on Israeli targets in southern Lebanon and northern Israel were "a legitimate response to the enemy's persistent violations of the ceasefire since the first day of the announcement of the temporary truce".

United Nations Special Coordinator for Lebanon Jeanine Hennis-Plasschaert began Sunday an official visit to Israel where she is scheduled to meet with senior Israeli officials.

Discussions will focus on opportunities to consolidate the cessation of hostilities and pave the way to lasting stability for communities in Lebanon and northern Israel.