U.S. mediator Amos Hochstein on Tuesday said "restoring calm on the southern border" of Lebanon with Israel is "of utmost importance to the United States."

"It should be the highest priority for both Lebanon and Israel," Hochstein urged after meeting Speaker Nabih Berri in Ain el-Tineh after he arrived in Lebanon on a surprise visit.

The Israeli war cabinet has discussed a mechanism for avoiding being dragged into wars on other fronts, specifically with Lebanon, Al-Jazeera television reported.

A Lebanese woman and her three granddaughters were laid to rest in their hometown in southern Lebanon on Tuesday, two days after they were killed in an Israeli drone strike that hit the car they were traveling in near the Lebanon-Israel border.

Hundreds of men and women marched before the four coffins, which were draped in black and white banners as they were carried through the streets of the village of Ainata. The coffins were later taken for burial in a cemetery in the nearby village of Blida.

Israel bombed Tuesday al-Labbouneh, near the southern Lebanese town of Naqoura, and the outskirts of the southern towns of Mhaibib and Aitaroun, as two Iron Dome missiles landed in an open area in the outskirts of the town of al-Tiri in south Lebanon after a failed interception attempt.

Meanwhile, Israeli media said that Israeli residents of the Galilee Panhandle near Lebanon's border had been asked to stay near shelters over a suspected security incident.

Hamas militants on Monday fired 16 rockets from south Lebanon towards northern Israel, the Palestinian group's armed wing announced, saying they targeted areas south of the Israeli coastal city of Haifa.

The Ezzedine al-Qassam Brigades said the strikes came "in response to the occupation's (Israel's) massacres and its aggression against our people in the Gaza Strip."

Hamas political bureau chief Ismail Haniyeh will arrive in Beirut within days, following his visit Sunday to Iran and his meeting with its supreme leader Ayatollah Ali Khamenei, media report said.

A highly informed source meanwhile told the Nidaa al-Watan newspaper that former General Security chief Abbas Ibrahim’s “presence in Qatar to take part in the ongoing negotiations over the prisoner swap file between Hamas and Israel is direct intervention by Hezbollah in this file.”

Israel shelled Monday the outskirts of the southern border towns of Alma al-Shaab, al-Naqoura, and al-Khiyam.

Meanwhile, Israeli residents near Lebanon's border have been asked to stay home over a suspected security incident.

Students in Lebanon observed Monday a moment of silence for Rimas, Taline and Layan, ages 10, 12 and 14, and their grandmother who were killed Sunday evening by an Israeli airstrike in the southern town of Ainata.

The death of the three children and their grandmother raised the number of civilians killed on the Lebanese side in the border clashes between Hezbollah and Israel to at least 14, despite Hezbollah's warning that if Israel kills Lebanese civilians, it will be considered a violation of the rules of engagement and it will retaliate by attacking civilian targets.

All the ongoing military developments and diplomatic efforts do not indicate that there will be any imminent agreement on a ceasefire in Gaza or on Lebanon’s southern front, informed political sources said.

Such an agreement will not be reached before the emergency Arab summit that will be held in Riyadh on November 11, the sources added, in remarks to al-Joumhouria newspaper published Monday.

The British Foreign Office said on Monday it was pulling out some of its embassy staff from Lebanon over fears that Israel's war against Hamas in the Gaza Strip could widen into the region.

"Events in Lebanon are fast moving. The situation has potential to deteriorate quickly and with no warning," the Foreign Office said in updated travel advice for Lebanon.