At least 100 people died on Sunday, according to the Lebanese health ministry, following Israeli airstrikes.
Israel special forces have today crossed the border into Lebanon, with elite troops entering Hezbollah tunnels.
It comes ahead of a possible wider ground invasion later this week.
An Israeli official said they were targeting Hezbollah infrastructure, including weapons sites and command and control centres, in a bid to push the militants away from the Israeli border.
The official said: “They are targeting key sites which have been built across the border zone.
“The question now is what the US will do, and I just hope the US doesn’t get involved and pull us back.”
The move comes in the wake of its assassination of leader Hassan Nasrallah in an attempt to leverage its advantage.
Israel’s defence minister has hinted that a ground operation against Hezbollah in Lebanon is being prepared.
Yoav Gallant told Israeli troops: “Nasrallah’s elimination is an important step but it is not the end – to return the residents of the north safely to their homes we will activate all our capabilities – including you.”
On Sunday, Israel ombarded Houthi targets in both Yemen and Lebanon.
Dozens of Israeli warplanes targeted the port of Hodeidah, attacking fuel facilities, power plants and ship docking sites. Houthi media said the strikes killed four people and wounded 33.
At least 100 people died on Sunday, according to the Lebanese health ministry, and a minister warned that the country was on the brink of catastrophe.
The United States has issued a last-minute appeal to both sides for restraint, warning Benjamin Netanyahu that war would not return 60,000 displaced Israelis to their homes in the north of the country.