U.S. President Donald Trump said Tuesday he had suggested to Israel that Syrian President Ahmed al-Sharaa should deal with Lebanon's Iran-backed Hezbollah seeing as the Israeli campaign was causing too many casualties.

Iran's Foreign Minister Abbas Araghchi said on Tuesday that ending the war on all fronts, including Lebanon, was "the most important" issue in the peace deal with the United States announced the day before.

Iran's top negotiator Mohammad Bagher Ghalibaf will attend the signing in Switzerland of the deal ending the war with the United States, an Iranian deputy foreign minister said on Tuesday.

Israeli Prime Minister Benjamin Netanyahu on Monday said he intended to run in elections scheduled for later this year, as he faced domestic criticism over his wartime leadership.

Israeli Prime Minister Benjamin Netanyahu said on Monday that Israel's forces would remain in Gaza, Lebanon and Syria "for as long as necessary," hours after a deal was announced between Iran and the U.S. to end the Middle East war.

Israeli Prime Minister Benjamin Netanyahu said Monday that the joint U.S.-Israeli military campaign against Iran had spared his country from what he described as the Islamic republic's threat of "nuclear annihilation".

Hezbollah said on Monday it had repelled an Israeli force that was trying to "advance" in southern Lebanon, despite the U.S.-Iran agreement to end the Middle East war on all fronts including in Lebanon.

The Iran-backed group said the attack came in response to Israel's violation of the ceasefire on Monday.

President Joseph Aoun on Monday welcomed the announced U.S.-Iran deal to end the Middle East war during a call from Tehran's top diplomat and foreign minister Abbas Araghchi, the Lebanese presidency said in a statement.

The Lebanese leader said he hoped the agreement would be a "positive step towards reducing tensions and opening the door to diplomatic solutions," while Araghchi emphasized "the importance of respecting Lebanon's sovereignty and territorial integrity by all parties," the statement said.

When Kamal Kamal heard a ceasefire deal had been agreed between Iran and the United States, he rushed back to the southern city of Nabatieh only to find an Israeli strike had reduced his life's work to rubble.

A deal between Washington and Tehran that ends the Israel-Hezbollah war leaves many issues in Lebanon unresolved, failing to mention Israel withdrawing from the country or an end to Tehran's support for the militant group.