Israel's two far-right ministers on Monday called for an escalation of military operations in Lebanon, with one advocating strikes on Beirut in response to Hezbollah's drone attacks.

Israeli Chief of Staff Eyal Zamir said in a limited security meeting on Sunday night that "buildings in Beirut should be attacked in response to Hezbollah's drone attacks," Israel's public broadcaster quoted informed sources as saying.

U.S. Secretary of State Marco Rubio said Monday that a deal to end the war with Iran could materialize "today", adding that Israel had the right to defend itself against attack.

"We thought we might have some news last night, maybe today, I wouldn't read too much into it," Rubio said in New Delhi, referring to the potential agreement.

Israel said on Monday a soldier was killed in southern Lebanon, taking to 23 the number of its troops killed in the war with Hezbollah.

Israel's military warned residents of 10 villages, most of them in southern Lebanon, on Monday to evacuate their homes ahead of expected strikes against alleged Hezbollah targets.

"In light of Hezbollah's violation of the ceasefire agreement, the Israel Defense Forces (army) are compelled to operate against it with force," the military's Arabic-language spokesman, Avichay Adraee, said in a social media post, listing the names of the villages.

President Joseph Aoun on Monday said Israel's withdrawal from the country's south was a "non-negotiable" demand that authorities would pursue through negotiations, days ahead of a new round of talks in Washington.

In a statement commemorating Israel's previous withdrawal from south Lebanon in 2000 after some two decades of occupation, Aoun said that "this year, the anniversary of the liberation comes as Lebanon is weighed down by a painful reality."

U.S. Secretary of State Marco Rubio accused Hezbollah in a statement Sunday of trying to plunge Lebanon "back into chaos."

Lebanon's health ministry said two people including a paramedic from the Hezbollah-affiliated Islamic Health Committee were killed Sunday in Israeli strikes on the south that also wounded six other rescuers.

Hezbollah chief Naim Qassem expressed hope Sunday for an agreement between Iran and the United States and that Lebanon, where Israel and the Iran-backed group are at war, would be part of its terms.

Israeli Prime Minister Benjamin Netanyahu said on Sunday he and U.S. President Donald Trump had agreed that any final deal with Iran must fully end the Islamic republic's "nuclear threat".