Hezbollah said on Wednesday its fighters had pushed back advancing Israeli troops in clashes along the length of the border, a day after Israel said it had killed two successors to the Iran-backed Lebanese militant movement's slain leader.

Hezbollah has been launching rockets against Israel for a year in parallel with the Gaza war and is now fighting it in ground clashes that are spreading along Lebanon's mountainous frontier with Israel.

The group said it had fired several rocket salvos at Israeli troops near the village of Labbouneh in the western part of the border area, close to the Mediterranean coast, and had managed to push them back.

Further east, it said it had attacked Israeli soldiers in the village of Maroun el-Ras and fired missile barrages at Israeli forces advancing toward the twin border villages of Mays al-Jabal and Mouhaybib.

Rocket sirens sounded constantly across northern Israel on Wednesday, including in the major port city of Haifa, following heavy fire from Lebanon. Israel's military said about 40 projectiles were launched in one barrage at Haifa, some of which were intercepted while others fell in the area.

Israeli ambulance workers said two people were killed in strikes on Kiryat Shmona near the border and at least six were wounded in Haifa.

Separately, at least six people were wounded, two of them seriously, in a stabbing attack in the Israeli city of Hadera on Wednesday.

Israeli police said the six victims were attacked over four separate crime scenes. The police did not immediately provide other details, but issued a brief video of the suspected attacker being apprehended.

Of the six people rushed to the hospital, at least two were in serious condition, according to medical officials.

Deadly Israeli airstrikes in Lebanon continue

The escalation in Lebanon, after a year of war between Israel and Hamas in Gaza, has raised fears of a wider Middle East conflict that could suck in Iran and Israel's superpower ally the United States. Iran fired a barrage of missiles at Israel last week, with Israel aided in its air defence by a number of allies.

The Middle East has been on edge awaiting Israel's response to the strike, which Tehran carried out in retaliation for Israel's escalation in Lebanon. Biden has said Israel should consider alternative targets to striking Iranian oil fields or nuclear sites.

WATCH l Explaining the challenges and perils of hitting Iranian nuclear site:

Will Israel attack Iran’s nuclear facilities? | About That

Prime Minister Benjamin Netanyahu has called Iran's ballistic missile strike against Israel a 'big mistake' vowing to retaliate. Andrew Chang breaks down Israel's potential response and the likelihood that Iran's nuclear facilities, oil refineries, and military infrastructure and leaders could be targeted.

U.S. President Joe Biden is expected to speak on Wednesday with Israeli Prime Minister Benjamin Netanyahu about possible Israeli retaliation on Iran for an Iranian missile strike last week.

In recent weeks Israel has carried out a string of assassinations of top Hezbollah leaders and launched ground operations into southern Lebanon that expanded further this week.

Israel launched airstrikes Wednesday including at targets far from the border combat zone. The Lebanese health ministry said four people were killed and 10 wounded by a strike that hit the town of Wardaniyeh, north of Sidon along the coast.

Israel has said that troops from as many as four divisions have operated inside Lebanon since the first announcement of the ground operation on Oct. 1. It has not confirmed that they have established a permanent presence there.

Israel's bombardment of Lebanon has killed more than 2,100 people, most of them in the last two weeks, and forced 1.2 million people from their homes. Israel says it has no choice but to strike Hezbollah so that tens of thousands of Israelis can return to homes they fled under Hezbollah rocket fire.

Burn victims from Israeli strikes are being treated at a specialized unit in Beirut's Geitaoui hospital, the only one of its kind in the country. Reuters journalists saw nurses gently change the gauze on patients, some of whom were wrapped neck down because of the severity of burns.

Mahmoud Dhaiwi, a Lebanese soldier, told Reuters he was off duty and heading to the beach when his car was hit by an Israeli strike. His whole body was burned.

Overnight, Israel again bombed Beirut's southern suburbs and said it had killed a figure responsible for budgeting and logistics for Hezbollah, Suhail Hussein Husseini.

The densely populated and thriving suburban district has been abandoned by many residents following Israeli evacuation warnings. Some Lebanese draw parallels between the warnings and those seen in Gaza over the last year, prompting fears that Beirut could face the same scale of destruction.