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."

Iran warned Monday that, while some progress had been made, it was not yet close to striking a deal with the United States to end the Middle East war, after a weekend of mixed messages from Washington and Tehran.

World oil prices tumbled on renewed optimism about an agreement, after top U.S. diplomat Marco Rubio suggested a deal could be reached within the day -- but Iran's foreign ministry spokesman responded: "No one can make such a claim."

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".

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.

U.S. President Donald Trump has assured Israeli Prime Minister Benjamin Netanyahu he will hold firm on his demand for the dismantling of Iran's nuclear program as a condition in any final agreement with Tehran, a senior Israeli official told AFP on Sunday.

Israeli strikes hit Lebanon on Sunday, both before and after Israel's military issued an evacuation warning for 10 villages in the south and east, state media reported.

U.S. President Donald Trump said Sunday that he had told U.S. negotiators "not to rush into a deal" with Iran, amid anticipation that an agreement to end the war in the Middle East was close.

"The negotiations are proceeding in an orderly and constructive manner, and I have informed my representatives not to rush into a deal in that time is on our side," Trump wrote on his Truth Social account.