The Israeli military has begun a “limited, localised and targeted” ground operation against Hezbollah in southern Lebanon, it has said, as it continued shelling areas close to the border and carrying out airstrikes on the capital, Beirut.

“The IDF [Israel Defense Forces] began limited, localised, and targeted ground raids based on precise intelligence against Hezbollah terrorist targets and infrastructure in southern Lebanon,” the military said in a statement on X early on Tuesday.

“These targets are located in villages close to the border and pose an immediate threat to Israeli communities in northern Israel,” it continued, adding: “Operation ‘Northern Arrows’ will continue according to the situational assessment and in parallel to combat in Gaza and in other arenas.”

Hezbollah leader Hassan Nasrallah was killed by an Israeli strike on Beirut on Friday, dealing a heavy blow to the militant group and raising fears that Israel might be preparing for a ground offensive in Lebanon, and that conflict could spread across the Middle East. Israel has since continued pounding Beirut and also launched strikes on Yemen and Syria.

Tuesday’s statement from the IDF followed Israeli media reports that the country’s cabinet had approved the next stage of its operation in Lebanon after a meeting chaired by the prime minister, Benjamin Netanyahu.

Hours earlier, US and other officials also said that Israeli forces appeared to have launched what sources called “limited ground operations” inside southern Lebanon.

“This is what they have informed us that they are currently conducting, which are limited operations targeting Hezbollah infrastructure near the border,” the US state department spokesperson, Matthew Miller, told journalists.

Early on Tuesday, Lebanon’s health ministry said at least 95 people had been killed and 172 wounded in Israeli strikes on Lebanon’s southern regions, the eastern Bekaa Valley, and Beirut in the past 24 hours.

Hezbollah’s deputy leader, Naim Qassem, in a first public speech on Monday since Nasrallah’s death, said that “the resistance forces are ready for a ground engagement”.

Heavy shelling into Lebanon was taking place along the boundary in the area north of Kiryat Shmona, in an area where Israeli armour and infantry advanced into Lebanon during the 2006 war. Airstrikes continued in Beirut and in at least 10 locations across the south of the country, according to Lebanon’s state news agency.

The Israeli military later declared areas of Metula, Misgav Am and Kfar Giladi in northern Israel a closed military zone.

The US president, Joe Biden, said earlier he was aware of Israel’s plans to launch an operation into Lebanon as he urged against such a move. “I’m more aware than you might know and I’m comfortable with them stopping,” he told reporters at the White House. “We should have a ceasefire now.”

The towns of Marjayoun, Wazzani and Khiam – which sit in a series of interlocking valleys overlooked by steep slopes – were being shelled on Monday night.

One resident in Marjayoun said that a local official had received a phone call ordering residents to evacuate but shelling had started before people could leave the town. “They called the mukhtar of Marjayoun, and told us we needed to evacuate. But we can’t move, the roads are filled with shelling and airstrikes,” the resident said.

An hour later, the road leading out of Marjayoun was hit by an Israeli airstrike and rendered inoperable, Lebanon’s National News Agency reported.

The area, with its scattered villages, and scrubby landscape hiding bunkers and combat tunnels, has long been a base for Hezbollah fighters and was heavily fought over during the last war between Israel and Hezbollah 18 years ago.

Hezbollah said in a statement that it had targeted a group of Israeli soldiers who were in the “orchard” near the Lebanese border towns of Odaisseh and Kafr Kila, “achieving confirmed casualties”. Kafr Kila is one of the towns that borders the area that Israel declared a closed military zone on Monday.