Israel's army chief told soldiers on Wednesday to prepare for a possible ground offensive against Hezbollah in Lebanon as US President Joe Biden warned against "all-out war" in the Middle East.

"We are attacking all day, both to prepare the ground for the possibility of your entry, but also to continue striking Hezbollah," Lieutenant General Herzi Halevi told a tank brigade, a statement from the military said as Israeli warplanes conducted hundreds of deadly strikes around Lebanon.

Prime Minister Benjamin Netanyahu said Israel's military operations against Hezbollah would not stop until northern residents can safely return to their homes.

Israel's warnings came after Hezbollah said it had targeted Israel's Mossad spy agency headquarters on Tel Aviv's outskirts -- the first time it has fired a ballistic missile in almost a year of cross-border clashes sparked by the Gaza war.

Lebanon's health minister said retaliatory Israeli strikes killed 51 people and injured 223, including in mountainous areas outside Hezbollah's traditional strongholds.

Israel said it hit 60 Hezbollah intelligence sites, among hundreds of the group's targets struck across Lebanon.

In Washington, President Biden warned of the possibility of "all-out war" after Israel's troops were put on alert for a possible ground operation.

"An all-out war is possible," Biden told broadcaster ABC.

"What I think is, also, the opportunity is still in play to have a settlement that could fundamentally change the whole region."

Biden added that there was a "possibility" of a Lebanon ceasefire, but "I don't want to exaggerate it".

The United States is Israel's main backer, and Biden said earlier on Wednesday that a "full-scale war is not in anyone's interest".

Cross-border clashes intensified on Wednesday after Israeli raids on Monday killed at least 558 people in the deadliest day of violence in Lebanon since its 1975-90 civil war.

In Tel Aviv, sirens sounded following Hezbollah's unprecedented missile launch at dawn.

US National Security Council spokesman John Kirby called Hezbollah's attack on Tel Aviv "deeply concerning", but added there was "still time and space for a diplomatic solution here to de-escalate the tensions and to prevent an all-out war".

The Israeli military said "over 280 Hezbollah" targets had been struck across Lebanon on Wednesday, and added the strikes were ongoing.

"Fighter jets struck 60 terrorist targets belonging to Hezbollah's intelligence directorate," the army said.

It said two reserve brigades were being called up "for operational missions in the northern arena", adding this would "enable the continuation of combat against the Hezbollah terrorist organisation".

The UN Security Council said it would hold an emergency meeting on the crisis in New York later Wednesday, as UN chief Antonio Guterres warned the situation was critical.

"We should all be alarmed by the escalation. Lebanon is at the brink," he said.

The UN's International Organization for Migration on Wednesday said 90,000 people had been displaced in Lebanon so far this week. (AFP)