Israeli tanks are reportedly massing along the Lebanon border, fuelling fears of ground invasion.
Fresh airstrikes were also launched against Houthi targets in Yemen on Sunday.
Troops and tanks were seen gathering in the north of Israel on the border with Lebanon, according to international media reports.
Another media report says Lebanon’s Ministry of Public Health confirmed another 105 people were killed and 359 wounded in fresh Israeli air raids on Lebanon.
The Yemeni port city of Hodeidah was attacked, targeting key infrastructure including the Ras Isa seaport and power stations.
International media outlets earlier say the Iran-backed group’s long-time leader, Hassan Nasrallah, was killed on Friday at the start of almost 48 hours of incessant airstrikes.
US media reports said scores of top commanders and officials were killed alongside Nasrallah.
At the United Nations, Secretary-General Antonio Guterres says he holds grave concerns about the “dramatic escalation” in Beirut.
“This cycle of violence must stop now and all sides must step back from the brink,” he says.
“The people of Lebanon, the people of Israel, as well as the wider region, cannot afford an all-out war.”
Guterres wants all parties to recommit to the full implementation of UN Security Council resolution 1701 (2006) and an immediate ceasefire.
He also repeated a call for another ceasefire in Gaza and the release of all hostages.
ABC News reported that the Lebanese PM said almost one million people are feared displaced across Lebanon due to the attacks on Hezbollah.
On Sunday, Lebanon’s caretaker prime minister Najib Mikati said his country could be witnessing its largest wave of displacement ever amid intense Israeli air strikes.
“It is the largest displacement movement that may have happened … in Lebanon,” Mikati told reporters.
Up to one million people could be forced to flee, he said, roughly one-fifth of Lebanon’s population.