The Iran-backed group, which has been launching rockets against Israel for a year in parallel with the Gaza war and is now fighting it in ground clashes, said it had pushed the troops back.
The escalation in Lebanon and the ongoing one-year-old 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.
The Israeli military said three of its troops were severely injured on Tuesday and Wednesday during combat in southern Lebanon.
Sirens sounded in northern Israel on Wednesday morning after Israel renewed bombing of Beirut's southern suburbs, a Hezbollah stronghold, overnight.
Israel renewed its bombing of Beirut's southern suburbs, a Hezbollah stronghold, overnight. (AP PHOTO)
The conflict in Lebanon has escalated dramatically in recent weeks as Israel has carried out a string of assassinations of top Hezbollah leaders and launched ground operations into southern Lebanon that expanded further this week.
An Israeli military spokesperson declined to say how many troops were in Lebanon but the military has announced four divisions are operating on the border, meaning that thousands of soldiers are deployed.
Overnight, Israel again bombed Beirut's southern suburbs and said it had killed a figure responsible for budgeting and logistics, Suhail Hussein Husseini.
Many Lebanese draw parallels between the warnings and those seen in Gaza in the past year, prompting fears Beirut could face the same scale of destruction.
US President Joe Biden is expected to speak on Wednesday with Israeli Prime Minister Benjamin Netanyahu, with talks set to include discussion of any plans to strike Iran.
The Middle East has been on edge awaiting Israel's response to a missile attack from Iran last week that Tehran carried out in retaliation for Israel's military escalation in Lebanon.
The Iranian attack ultimately killed no one in Israel and Washington called it ineffective.
Many Lebanese fears Beirut could face the same scale of destruction as Gaza. (AP PHOTO)
Israel's retaliation would be a key subject of the call, with Washington hoping to weigh in on whether the response is appropriate, a person briefed on the discussions said.
Biden has said he would think about alternatives to striking Iranian oil fields if he were in Israel's shoes.
Last week, he also said he would not support Israel striking Iranian nuclear sites.
The bombardment has left more than 2100 people dead in Lebanon, most of them in the past two weeks, and displaced roughly 1.2 million across the country.
Netanyahu said on Tuesday Israeli air strikes had killed two successors to Hezbollah's slain leader Sayyed Hassan Nasrallah, killed in an Israeli air attack on Beirut's southern suburbs on September 27.
Netanyahu did not name them, but Israeli Defence Minister Yoav Gallant said Hashem Safieddine, the man expected to succeed Nasrallah, had probably been "eliminated".
It was not clear whom Netanyahu meant by the second replacement.
Israel's bombardment has displaced roughly 1.2 million across Lebanon. (AP PHOTO)
Hezbollah deputy leader Naim Qassem said on Tuesday the group's capabilities were intact despite the "painful blows" inflicted by Israel's mounting military pressure.
Qassem said the group endorsed efforts by Lebanon's Speaker of parliament to secure a ceasefire, and conspicuously left out an oft-repeated condition of the group - that a Gaza ceasefire would have to be reached before Hezbollah put down its arms.
Netanyahu's office declined to comment on Qassem's remarks.
US State Department spokesman Matthew Miller told reporters that Hezbollah had "changed their tune and want a ceasefire" because the group is "on the back foot and is getting battered" on the battlefield.
Hezbollah is the most formidably armed of Iran's proxy forces across the Middle East and has been acting in support of Palestinian militants fighting Israel in Gaza.
The heightened regional tensions kindled a year ago by Palestinian armed group Hamas's attack from Gaza on southern Israel have escalated to include Lebanon and prompt several direct confrontations between Israel and Iran.
On October 1, Iran fired missiles at Israel. On Tuesday, Iran warned Israel not to follow through on threats of retaliation.
