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 from hits overnight and during Thursday to 28.
The strike killed the head of one of Hezbollah's air force units, Mohammad Surur, two security sources said, the latest senior Hezbollah commander to be targeted in days of assassinations hitting the group's top ranks.
Smoke was seen rising after the hit near an area where several Hezbollah facilities are located and many civilians also live and work.
Hezbollah's al-Manar TV broadcast images of a damaged upper floor of a building.
Israel's aerial defence system has ensured that Hezbollah rockets have done limited damage. (AP PHOTO)
On the Israeli side of the border with Lebanon, the army staged an exercise simulating a ground invasion - a potential next stage after relentless air strikes and explosions of communications devices.
Israel's air force is planning to assist troops in the event of a ground operation and will stop any arms transfers from Iran, Air Force Commander Major General Tomer Bar said.
"We are preparing shoulder to shoulder with Northern Command for a ground maneuver. Prepared, if activated. This is a decision to be made above us," he told soldiers, in a video distributed by the Israeli military.
Israel has vowed to secure its north and return thousands of citizens to communities there who have fled since Hezbollah launched a campaign of cross-border strikes last year in solidarity with Palestinian militants fighting in Gaza.
Landing in the United States to address the United Nations General Assembly, Israeli Prime Minister Benjamin Netanyahu told reporters the military will keep hitting Hezbollah with "full force and we will not stop until we achieve all our goals, first and foremost returning the residents of the north safely to their homes".
Israel's stance has dashed hopes for a swift settlement after Lebanese Prime Minister Najib Mikati, whose government includes Hezbollah elements, had expressed hope for a ceasefire.
Hundreds of thousands of people have fled their homes during the heaviest Israeli bombardment of Lebanon since a major war in 2006.
Hezbollah has faced off against the Israeli military since the Shi'ite Muslim movement was created by Iran's Revolutionary Guards in 1982 to counter an Israeli invasion of Lebanon.
The US, France and several other allies including Australia urged an immediate 21-day ceasefire across the Israel-Lebanon border.
They also expressed support for a ceasefire in the Gaza Strip.
The White House said that discussions are continuing for a 21-day ceasefire and US and Israeli officials would hold talks in New York on Thursday.
US Secretary of State Antony Blinken was scheduled to meet with Israeli Minister for Strategic Affairs Ron Dermer.
In London, US Defense Secretary Lloyd Austin warned there was a risk of all-out war in the Middle East but a diplomatic solution was still possible.
"So let me be clear, Israel and Lebanon can choose a different path, despite the sharp escalation in recent days, a diplomatic solution is still viable," Austin said.
More than 600 people have been killed since Monday in Israel's strikes on Lebanon.
Hezbollah has fired hundreds of missiles at targets in Israel including its commercial hub Tel Aviv, although Israel's aerial defence system has ensured that the damage has been limited.
Israeli fighter jets on Thursday also hit infrastructure on the Lebanese-Syrian border to stop the transfer of weapons from Syria to Hezbollah in Lebanon, Israel's military said.
The Lebanese health ministry said most victims on Thursday were Syrians killed in the town of Younine in the Bekaa Valley.
Lebanon is home to about 1.5 million Syrians who fled the conflict there.
Hezbollah said in a statement it had struck the town of Kiryat Shmona in north Israel and an Israeli military northern command base as well as using air defence weapons to force two Israeli warplanes back.
