The U.S. has promised to convince Israel’s government to agree to a brief humanitarian truce in the war on Gaza and the discussions are now revolving around what can be done during the proposed pause, informed Palestinian sources quoted Arab and regional capitals as saying.

“The discussions are focusing on an incomplete exchange of civilian captives held by the resistance forces in Gaza in return for the entry of a large quantity of aid into Gaza, including fuel, and helping in addressing the file of those trapped under the rubble,” the sources told al-Akhbar newspaper in remarks published Wednesday.

The parliamentary bloc of the Free Patriotic Movement has reiterated its objection to the extension of the term of Army chief Gen. Joseph Aoun ahead of his planned retirement in January, considering it "unconstitutional."

"There are legal solutions to avoid the vacancy," the Strong Lebanon bloc said in a statement Tuesday.

Israeli Defense Minister Yoav Gallant announced Tuesday that Israel does not have "any intention to fight a war against Hezbollah."

He however warned that if Hezbollah chief Sayyed Hassan Nasrallah "commits a mistake" he will be "destroying Lebanon."

Hezbollah said Tuesday that it fired rockets at Israel's artillery positions in the occupied Golan Heights in response to an overnight Israeli strike on a Hezbollah post on the outskirts of the town of Aramta in the Iqlim al-Tuffah region.

Aramta lies about 20 kilometers north of the border and is a Hezbollah stronghold. The strike was one of the deepest inside Lebanon since the fighting along the border erupted on October 8.

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.

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.

CIA Director William Burns is in the Middle East meeting with intelligence partners and leaders of several countries on matters including ones related to the war between Israel and Hamas, a U.S. official said.

Topics include the fate of some 240 people being held hostage by the Hamas militant group in Gaza, and the U.S. commitment to prevent state and nonstate actors from widening the Israel-Hamas war regionally, the U.S. official said.

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."

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.