Israeli Defense Minister Yoav Gallant said Thursday that he has approved more “offensive operations” in Lebanon, together with the army chief, the head of the intelligence division and the head of the army’s operations division.

The Israeli military said Thursday its latest strike on south Beirut killed Mohammad Srour, the head of Hezbollah's drone unit, who a source close to the group had earlier said was the target.

"Following precise intelligence guidance from the Air Force and the Intelligence Division, fighter jets targeted and eliminated (Srour), the commander of Hezbollah's air unit, in Beirut," a military statement said.

Inflexible stances by Israel and Hezbollah have torpedoed a comprehensive solution for the current escalation and made efforts instead focus on a “temporary ceasefire” that would give a chance to further negotiations, an informed Lebanese source said.

Families of Israeli hostages still held in Gaza for nearly a year are urging Israel to ensure than any possible cease-fire deal with Hezbollah includes provisions for the war in Gaza.

Gil Dickmann, whose cousin, Carmel Gat, was kidnapped and was one of six Israelis killed in Hamas tunnels in August, said the families of the hostages are feeling forgotten as attention shifts to the northern front.

The Israeli military said on Thursday that its fighter jets struck infrastructure on the Syria-Lebanon border used by Hezbollah, as cross-border attacks continued amid calls for a ceasefire.

"A short while ago, (Israeli air force) fighter jets struck infrastructure along the Syria-Lebanon border used by Hezbollah to transfer weapons from Syria to Hezbollah in Lebanon, which the terrorist organization used against Israeli civilians," a military statement said.

The diplomatic efforts are advancing and expect a Lebanon-Israel ceasefire soon, sources informed on the negotiations in New York told Lebanon’s MTV on Thursday.

Israel flatly rejected on Thursday a push led by key backer the United States for a 21-day ceasefire in Lebanon, as it vowed to keep fighting Hezbollah militants "until victory".

Israeli aerial bombardment of Hezbollah strongholds around Lebanon has killed hundreds of people this week, while the militant group has hit back with barrages of rockets.

Britain says it’s sending $6.7 million worth of humanitarian assistance, including medical supplies, hygiene kits and fuel to Lebanon to support the civilian population there as fighting forces thousands to flee their homes.

The United Kingdom said in a statement that the United Nations agency for children, UNICEF, will distribute the supplies, which will also help aid workers better deal with urgent health and nutrition needs.

Israeli Prime Minister Benjamin Netanyahu said on Thursday his government had not responded to a push by the United States and its allies for a 21-day ceasefire in Israel's fight with Lebanese armed group Hezbollah.

"It is an American-French proposal, which the prime minister has not even responded to," said a statement from Netanyahu's office, adding that he had ordered the army "to continue the fighting with full force".

Families fleeing the escalating conflict in Lebanon have poured into Syria in growing numbers, waiting for hours in heavy traffic to reach the relative safety of another war-torn country.

U.N. officials estimated that thousands of Lebanese and Syrian families had already made the journey. Those numbers are expected to grow as Israel targets southern and eastern Lebanon in an aerial bombardment that local officials say has killed more than 600 people this week, at least a quarter of them women and children.