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.

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

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."

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".

Lebanon's health ministry said Sunday that an Israeli strike the previous day in the country's south killed 11 people including six women and a child, despite a ceasefire in the Israel-Hezbollah war.