Israeli Prime Minister Benjamin Netanyahu said Hezbollah's rockets and drones were a key threat demanding military action, as Israel's army expanded strikes on Lebanon where authorities reported four dead on Monday despite a ceasefire.

Lebanese President Joseph Aoun said direct talks with Israel sought to end the Israel-Hezbollah war and that those who dragged Lebanon into it were the ones committing "treason" -- a jab at the Iran-backed group, which claimed several attacks on Israeli targets in south Lebanon on Monday.

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.

Israel and Hezbollah have traded blame over violations of the fragile 10-day ceasefire in Lebanon agreed earlier this month, which has since been extended, and attacks by both sides have continued.

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.

The Israeli military on Monday said it had begun hitting Hezbollah positions in the Bekaa region, amid a ceasefire that began earlier this month.

"The IDF has begun to strike Hezbollah infrastructure sites in the Bekaa valley and in additional areas across southern Lebanon," it said in a brief statement on social media.

President Joseph Aoun said Monday that negotiations with Israel are not treason and that "treason is dragging your country into war to serve foreign interests."

"Some criticize us for choosing to negotiate, claiming there is no national consensus," he said, clearly pointing at Hezbollah. "When you dragged the country into war, did you have national consensus then?" Aoun asked.

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.