Israel rejected global calls on Thursday for a ceasefire with Hezbollah.
The US and France sought to keep prospects alive for an immediate 21-day truce they proposed on Wednesday, and said negotiations continued, including on the sidelines of a United Nations meeting in New York.
An Israeli warplane struck the edges of the capital Beirut, killing two people and wounding 15, including a woman in critical condition, Lebanon's health ministry said. That took deaths overnight and on Thursday to 28 and over 600 since Monday.
The strike killed the head of one of Hezbollah's air force units, Mohammad Surur, Hezbollah said.
Arriving in New York before addressing the UN General Assembly on Friday, Israeli Prime Minister Benjamin Netanyahu told reporters the Israeli military will keep hitting Hezbollah with "full force and will not stop” until the residents of the north safely return to their homes.