Dimming hopes for a cease-fire, Israeli Prime Minister Benjamin Netanyahu said Thursday that Israel plans to continue striking Hezbollah "with full force" and will not stop until all of its goals are achieved.

Netanyahu spoke as he landed in New York to attend the annual U.N. General Assembly meeting and as U.S. and European officials were pressing for a 21-day halt in fighting between Israel and Hezbollah to give time for negotiations.

Israeli Strategic Affairs Minister Ron Dermer, who is close to Prime Minister Benjamin Netanyahu, informed U.S. mediator Amos Hochstein Thursday in New York that “Israel is continuing its war in Lebanon and will not agree to the presented proposals,” an Arab diplomat said.

Caretaker Prime Minister Najib Mikati has said that he has done “everything necessary to protect Lebanon” in the face of Israel’s escalation, noting that foreign and Arab powers have supported Lebanon’s stance.

An elderly French woman was killed this week when her home collapsed following an explosion in south Lebanon, the French foreign ministry said Thursday, as Israel presses a deadly air campaign against Hezbollah.

"We are sorry to announce the death on Monday of an 87-year-old fellow countrywoman in a village near the city of Tyre. The building where she lived collapsed following a large explosion nearby," the ministry said.

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.