Israel's military chief said on Sunday that Hezbollah had suffered a severe blow fighting Israeli forces and was now in a "very difficult position", as he met with troops in southern Lebanon.

He spoke as the United States and Iran held talks in Switzerland after signing a preliminary agreement to end the broader Middle East war, with the conflict in Lebanon threatening to derail the deal.

Israeli Prime Minister Benjamin Netanyahu said on Sunday that Israeli forces would remain in southern Lebanon "as long as necessary", while also vowing to prevent Iran from acquiring nuclear weapons.

"We will remain in the security zone in southern Lebanon for as long as necessary to protect the cherished residents of the north and all the citizens of Israel... Nothing will alter that commitment," Netanyahu said.

Hezbollah chief Sheikh Naim Qassem on Sunday rejected any Israeli security zone in Lebanon, after Israel's Prime Minister Benjamin Netanyahu vowed his troops would remain in the country's south for as long as necessary.

Israeli troops "remaining on Lebanese land is impossible. There are no security zones for Israel... we have a national army which deploys, and it is responsible for preserving sovereignty, and it is who we cooperate with," Qassem said in a televised address, adding that "Israel is an aggressor and must leave."

U.S. President Donald Trump said Sunday in a surprising statement that "Iran must immediately stop their highly paid PROXIES in Lebanon from causing trouble," apparently referring to Iran-backed Hezbollah.

Iran said on Sunday that the ongoing conflict in Lebanon between Israel and Hezbollah will top the agenda in talks with the United States in Switzerland, as well as issues such as frozen Iranian funds and the sale of the country's oil.

The Israeli military said that one of its soldiers was killed in fighting in southern Lebanon on Saturday, marking the fifth such fatality since a U.S.-Iran deal was reached to end the Middle East war.

Lebanon's central bank on Saturday condemned a "direct and deliberate" Israeli attack on one of its branches in the southern city of Nabatieh, where Israel had intensified its strikes despite a ceasefire.

Cautious calm has been engulfing south Lebanon since Saturday, after Israel's political leadership ordered its army to cease its operations, reportedly following intense U.S. pressure to do so.

U.S. Vice President JD Vance has said that Lebanon is one of "two big things" that will be discussed in the negotiations with Iran, as he departed from Washington for Switzerland.

Israeli Prime Minister Benjamin Netanyahu and Defense Minister Israel Katz on Saturday ordered the Israeli army to halt its operations in Lebanon while maintaining its positions, Israeli reports said.