The capital, Beirut, was struck for the third time in five days as the Israeli military said it had targeted and "eliminated" another key Hezbollah commander.

He was named by Israeli forces as Muhammed Qabisi - Hezbollah's commander in charge of missiles and rockets - and comes days after the militant group buried another of its top leaders.

There were multiple Israeli airstrikes across the south and in the east for a second day as huge swathes of the population continued fleeing to the north of the country.

Israel-Hezbollah latest updates

We saw terrified and worried families turning up at the emergency centre in Tyre as Israeli jets flew overhead alongside the sounds of Hezbollah rockets being fired into Israel.

"We have nothing left," a woman called Fatima told us. "We have no food, no water, nothing."

The UN refugee agency (UNHCR) said two of its workers had been killed in airstrikes, including a young mother and her son.

The agency said it was "outraged and deeply saddened" at the deaths.

Dina Daarwiche and her family were at home in the Bekaa Valley when the house was targeted.

She and her youngest son were killed and her husband and second child are critical in hospital.

The second UNHCR worker was named as Ali Basma, who had worked in the agency's Tyre office for seven years.

The Lebanese Ministry Of Health said the number killed in Monday and Tuesday's airstrikes included children and many women and had now risen to nearly 600.

UNHCR said in a statement: "The protection of civilians is a must.

"We reiterate the UN secretary-general's call for urgent de-escalation and calls on all parties to protect civilians, including aid workers in line with obligations under international humanitarian law."

We've been witnessing multiple airstrikes in the south throughout the day and evening with the constant sounds of blasts and ambulance sirens going off.

The head of Tyre's emergency response, Hassan Dbouk, told us: "Half of the IDPs (displaced people), they slept in the garden, on the beach, without any tent, any cover, any blanket, in the streets and in their cars, that's a disaster.

"And when you see the eyes of the babies and the women, it's really a disaster."

As desperate people turned up at the disaster response centre in Tyre, one man told us his was the only house still standing in his village.

"They hit them all," Abu Ali said.

The Israeli forces say they are targeting Hezbollah weapons stores, fighters and commanders and said the militant group is hiding in residential areas and using Lebanese people as human shields.

But Abu Ali insisted: "That's not true. Not a single target (in our village) was on a military position.

"They're only hitting civilians. We don't have military operations in our village."

The astonishing movement of tens of thousands of the Lebanese population from the south and along the border comes on the back of nearly a year of Israel saying it wants to create a buffer zone so Hezbollah cannot fire into its northern communities.

Even if the continuous Israeli bombardment of the south and the border is not a deliberate tactic to ensure this happens, that certainly appears to be the growing result.

But despite a range of Israeli attacks on its military command and supporters through the booby-trapped pagers and radios; despite its targeting of key Hezbollah commanders; and despite its aerial bombardment of multiple population centres and significant Hezbollah strongholds, the militant group shows no signs of backing down.

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Instead, the militants are using more of their powerful weapons.

Last night, for the first time, the group used a ballistic missile aimed at the suburbs of Tel Aviv, they say targeting a Mossad building, and in the last few days they have continuously fired their long-range Fadi rockets, which they have been launching deeper and deeper into Israeli territory.

The Iran-allied group, which the UK and US have designated as a terror group, has linked its attacks on Israel since last October to a Gaza ceasefire - and insists it will continue until there is one.

That's ensured its hero status among its many loyalists and its Hamas allies.

But with a Gaza ceasefire unlikely soon, and with the Israeli forces vowing to increase their onslaught on the militants, Lebanon looks set for a very rough period ahead.

The Sky News team reporting with Alex Crawford from south Lebanon is camera Jake Britton, specialist producer Chris Cunningham and Lebanon producers Jihad Jneid and Sami Zein.