Israel has warned that it will use “all the means” at its disposal to attack the Lebanese armed group Hezbollah amid growing fears of a ground assault on Lebanon.

“The next phase in the war against Hezbollah will begin soon,” Israeli Defence Minister Yoav Gallant told a meeting of local council heads in northern Israel on Monday, according to a statement from his office.

Earlier, Gallant told troops that Israel would “use all the means that may be required … from the air, from the sea, and on land.”

To allow displaced residents of the border area to return safely home, “we will employ all of our capabilities, and this includes you,” Gallant told troops.

Hezbollah began low-intensity strikes on Israeli troops a day after Israel launched its assault on Gaza last October in response to an attack by the Palestinian group Hamas.

Israel and Hezbollah have traded near-daily fire across the Israel-Lebanon border for almost a year, prompting tens of thousands of people on both sides to flee their homes. Israel’s military escalated the fighting this month, leaving people across the region fearful of even more violence to come.

Some Israeli forces have already conducted small-scale ground operations in Lebanon, several international media outlets reported, and Israel’s air force has bombarded targets across the country in recent days.

Israel has killed Hezbollah leader Hassan Nasrallah and several of the group’s top commanders in strikes on the southern suburbs of Beirut, and continued a campaign of air attacks on Hezbollah sites in eastern and southern Lebanon. More than 1,000 people have been killed since Israel escalated its attacks.

Hezbollah has continued to fire rockets and missiles at Israeli targets. On Monday, the Lebanese-armed group said its fighters targeted northern Israel’s Gesher Haziv settlement with a “salvo of rockets”.

In a statement, the Lebanese group said it also fired rockets at Israeli military positions in the occupied Golan Heights and fired a long-range anti-ship cruise missile at Kfar Giladi, a rural cooperative community known as a kibbutz.

In a separate statement, Hezbollah said it fired Fadi 1 missiles at areas in northern Haifa.

In the group’s first broadcast address since Nasrallah’s assassination, Hezbollah deputy chief Naim Qassem said it is prepared for any potential ground incursion and a long war.

When asked about reports that Israel is preparing for a “limited” ground invasion of Lebanon, US President Joe Biden called for a ceasefire.

Asked if he was comfortable with Israel’s plan, Biden replied: “I’m comfortable with them stopping.”

However, he did not elaborate on any plans to halt the conflict, or discuss US supplies of weapons and military aid to ally Israel.

Israel has told the US about a number of operations, the State Department said on Monday.

“I know I’ve seen reports about ground operations. We’ve had some conversations with them about that. They have at this time told us that those are limited operations focused on Hezbollah infrastructure near the border. But we’re in continuous conversations with them about it,” State Department spokesperson Matthew Miller told reporters.

Yossi Beilin, Israel’s former justice minister, told Al Jazeera that neither Hezbollah nor Israel “wants a ground battle” because “there is always a lethal price on both sides, people will be killed, and it should be prevented”.

He said that both sides need to renegotiate UN Resolution 1701, referring to the 2006 resolution to end the Israel-Hezbollah conflict at the time and pave the way for improved security along the border.

“I think we should rebuild the relations between Israel and Lebanon”, Beilin added.

Reporting from Marjayoun in southern Lebanon, Al Jazeera’s Imran Khan said that since the morning, Israeli air strikes have pounded the south of the country. He added that the Bekaa Valley, eastern Lebanon, as well as Baalbek and the road towards Syria have been hit.

“The death toll is climbing as well: 136 people killed in the last 24 hours, and that is something that is putting a tremendous amount of pressure on the emergency services. They’re simply running out of people and ambulances to be able to service the entire area,” he said.

Among those killed were three members of the Popular Front for the Liberation of Palestine group, who were targeted in the Kola area of Beirut in Israel’s first attack on the Lebanese capital beyond the southern suburbs.

Fatah Sharif, a Hamas top commander in Lebanon, was also killed along with his wife, son and daughter in an air strike on El Buss refugee camp, one of 12 dedicated to Palestinian refugees in Lebanon, in the southern port city of Tyre on Monday.

The Israeli military confirmed it had targeted him.

Sharif was also an employee of the United Nations Relief and Works Agency for Palestine Refugees (UNRWA), and was suspended from the agency earlier this year following allegations regarding his politics. The UNRWA chief has denied knowing that Sharif was a Hamas commander.

“I never heard the word ‘commander’ before,” Philippe Lazzarini told reporters in Geneva. “What’s obvious for you today, was not obvious yesterday.”

More than 100,000 people have fled to Syria from Lebanon since the escalation of the conflict between Israel and Hezbollah this month.

About 118,466 new displacements have occurred between September 23 and 27, the UN’s World Health Organization said in a situation report. The agency added that Lebanon’s health system also remains impacted and overstretched by a new escalation of violence in the country.

Lebanon’s acting Prime Minister Najib Mikati has said that the government is ready to fully implement the 2006 UN Security Council Resolution 1701 that aimed to end Hezbollah’s armed presence south of the Litani River as part of an agreement to stop war with Israel.