Israel's military says it has struck dozens of Hezbollah targets in southern Lebanon overnight and it is continuing to bomb targets. 

It came a day after it launched a wave of air strikes against the group, leading to Lebanon's deadliest day in decades.

"In the last hour, warplanes bombed Hezbollah targets in southern Lebanon, including missile launchers, military buildings, and buildings where weapons were stored," Israeli army spokesperson Avichay Adraee posted on X.

In a separate post, he added: "If you are near or inside Hezbollah buildings or those used by it to store weapons, you must move away from those buildings at least one kilometre away or outside the village immediately."

Israeli military chief of general staff Herzi Halevi said Hezbollah must not be given a break, and attacks on the Iran-backed group in Lebanon would be accelerated.

"The situation requires continued, intense action in all arenas," he said.

Later on Tuesday, the Israeli military confirmed it had conducted a targeted strike in Beirut but it provided no further details.

Lebanon's health ministry said so far six people had been killed in strikes on Beirut's southern suburbs and 15 people had been injured.

Hezbollah launches missiles at Israeli targets

On Tuesday morning local time, Iran-backed Hezbollah, said it had attacked several Israeli military targets, including an explosives factory 60 kilometres into Israel, with the Fadi series of rockets.

It said it attacked the explosives factory at about 4am and the Megiddo airfield three separate times overnight.

Hezbollah later announced the use of a new rocket — Fadi 3 — in an attack on an Israeli army base.

After almost a year of war against Hamas in Gaza on its southern border, Israel is shifting its focus to the northern frontier, where Hezbollah has been firing rockets into Israel in support of Hamas, also backed by Iran.

The Israeli military said it struck a Hezbollah militant cell and its artillery and tanks hit other Hezbollah targets in the south. 

Police in northern Israel said fragments of interceptor missiles were found in various areas.

On Tuesday, Lebanese authorities said Israeli air strikes on Monday had killed 558 people.

After some of the heaviest cross-border exchanges of fire since hostilities flared in October as the Gaza war erupted, Israel warned people in Lebanon to evacuate areas where it said Hezbollah was storing weapons.

Families from southern Lebanon loaded cars, vans and trucks with belongings and people young and old. Highways heading north were gridlocked.

The Lebanese minister coordinating the crisis response, Nasser Yassin, told Reuters 89 temporary shelters in schools and other facilities had been set up. 

He said they had capacity for more than 26,000 people fleeing what he called "Israeli atrocities".

Israel's military said it struck Hezbollah in Lebanon's south, east and north, including rocket launchers, command posts and militant infrastructure. 

The Israeli Air Force struck about 1,600 Hezbollah targets in southern Lebanon and the Bekaa Valley, it said.

Lebanon's Health Minister Firass Abiad said on Tuesday that at least 558 people had been killed since the Israeli strikes on Monday, including 50 children and 94 women, with 1,835 wounded.

One Lebanese official said it was Lebanon's highest daily death toll from violence since the 1975-1990 civil war.

Preparing for a ground invasion

Speaking to 7.30, Lebanon's Minister for Health, Firass Abiad, said the government feared a potential ground invasion from Israel.

"Israel have been threatening to do that for some time," Dr Abiad said.

"Looking at the progression of events … from last week into this week, I think that this is something that is on the table.

With residents from Lebanon's south already fleeing the area and the country in the midst of an economic crisis, Dr Abiad says the government is doing all it can to help people who may need to flee their homes.

"I shouldn't be preparing for civilian casualties, to be honest, in any conflict," Dr Abiad told 7.30.

"What we have been doing is raising the capacities of hospitals, making sure that the hospitals that are closer to the battlefronts are sort of … transferring patients away from them so that they are able to receive patients. 

"Also, we've been stocking up on medication and medical supplies."

Hezbollah's media office said on Tuesday that Israel was dropping leaflets with a "very dangerous" barcode on them onto Lebanon's eastern Bekaa Valley.

It warned that scanning the code with a phone would "withdraw all information" from any device.

There was no immediate comment from the Israeli military. Hezbollah's media office did not say if anything else was written on the flyers.

US seeks to de-escalate border tension

White House national security adviser Jake Sullivan said on Monday US President Joe Biden was determined to bring about a Gaza ceasefire and hostage deal with Hamas, and also de-escalate tensions on Israel's border with Lebanon.

"He absolutely hasn't given up," Mr Sullivan said in an interview with MSNBC.

He said there had been challenges getting both sides across the line "but we're determined to keep at it".

ABC/Reuters