Hezbollah vowed on Monday to keep fighting Israel and said it was ready to face any ground operation into Lebanon, after its leader was killed in an air strike that dealt the group a seismic blow.

In a televised address, the Iran-backed group's deputy chief Naim Qassem said a new leader to replace Hassan Nasrallah, who enjoyed cult status among his supporters, would be selected "at the earliest opportunity".

He also said the group was ready for any Israeli ground offensive, even though Israel's bombardment of its strongholds has in the past week killed a large number of its top commanders and officials.

Hezbollah began low-intensity cross-border strikes on Israeli troops a day after its Palestinian ally Hamas staged its unprecedented attack on Israel on October 7, triggering war in the Gaza Strip.

Israel said earlier this month that it was shifting its focus from Gaza to securing its northern border with Lebanon, in order to allow Israelis displaced since October to return to their homes.

It has also not ruled out a ground offensive in order to achieve its goals.

Israel's strikes on Lebanon have killed hundreds and forced hundreds of thousands more to flee their homes, and left people across the region fearful of more violence to come.

Qassem said Hezbollah would continue "confronting the Israeli enemy in support of Gaza and Palestine, in defence of Lebanon and its people, and in response to the assassinations and the killing of civilians".

Warning that any battle with Israel would be long, he said: "We will face any scenario and we are ready if Israel decides to enter by land, the resistance forces are ready for any ground confrontation."

On the other side of the border, Israel's Defence Minister Yoav Gallant told troops: "The elimination of Nasrallah is an important step, but it is not the final one."

"In order to ensure the return of Israel's northern communities, we will employ all of our capabilities, and this includes you," he said.

Most of Israel's strikes have targeted Hezbollah strongholds in eastern and southern Lebanon and the southern suburbs of Beirut, the group's main bastion.

On Monday, a drone strike hit a building in the Cola district in central Beirut, with an armed Palestinian group saying it had killed three of its members.

The strike, the first in the centre of the city in years, sparked panic, with 41-year-old resident Mohammed al-Hoss saying "the kids were in shock" after his house was damaged.

"We are with Gaza and support the Palestinian cause, but our country cannot cope with us going to war," he said.

"Our country is in a wretched state. They (Israel) finished with Gaza and they have come to Lebanon."

Lebanon's health ministry also reported the strike, saying it had killed four people and wounded four others. Israel has yet to comment.

Palestinian Islamist group Hamas later announced that its leader in Lebanon, Fatah Sharif Abu al-Amine, had been killed along with his wife and two children in another strike on Al-Bass refugee camp in south Lebanon.

The Israeli military confirmed it had "eliminated" Sharif in a strike.

Lebanon's health ministry said six rescuers affiliated with Hezbollah were killed in an Israeli strike Monday.

Around Lebanon, Israeli strikes killed more than 100 people on Sunday, including 45 near the southern city of Sidon, according to the ministry.

Lebanon's Health Minister Firass Abiad said Saturday that 1,030 people including 87 children had been killed since September 16.

UN refugee agency chief Filippo Grandi said "well over 200,000 people are displaced inside Lebanon", while more than 100,000 have fled to neighbouring Syria.

Prime Minister Najib Mikati said up to one million people may have been uprooted, in potentially the "largest displacement movement" in Lebanon's history.

The violence in Lebanon has raised fears of a much wider conflagration in the region.

On Monday, the Israeli army said it "successfully intercepted a suspicious aerial target that crossed from Lebanon into Israeli territory".

Israel said it also carried out strikes on Sunday targeting Iran-backed Houthis in Yemen that the rebels said killed four people and wounded 33. The raids in Yemen came a day after the Houthis said they launched a missile at Israel's Ben Gurion airport, trying to hit it as Prime Minister Benjamin Netanyahu was returning from New York.

Iran has said Nasrallah's killing would bring about Israel's "destruction", though the foreign ministry said Monday it would not deploy any fighters to confront Israel.

Lebanon began a three-day national mourning period for Nasrallah on Monday, with flags flying at half-mast.

In Israel, some had mixed feelings about the Hezbollah chief's killing.

"Nasrallah was responsible for the deaths of many Israelis, so it is good news," said Matan Sofer, 24, in the northern town of Rosh Pina.

"But do we risk it getting worse, who knows?"

(With Inputs From Agencies)