Israel and Hezbollah clashed overnight despite U.S. President Donald Trump's announcement that both sides had agreed to halt fighting ahead of U.S.-hosted talks between Israel and Lebanon on Tuesday.

Israel's growing offensive in Lebanon, including heavy bombardment and its deepest ground invasion in two decades, has threatened to scupper a ceasefire in the wider Middle East war between the United States and Iran.

France's foreign minister said Tuesday that nothing could justify Israeli troops remaining deep inside Lebanon, following the deepest incursion into Lebanese territory in two decades.

Israel and Hezbollah clashed overnight despite U.S. President Donald Trump's announcement that both sides had agreed to halt fighting ahead of U.S.-hosted talks between Israel and Lebanon.

Lebanon said an Israeli strike hit near a hospital in the southern city of Tyre on Monday as the health ministry shared footage showing heavy damage to the facility.

Iran's Revolutionary Guards threatened to open "new fronts" and keep the Strait of Hormuz closed over Israel's offensive in Lebanon, state media reported on Monday.

The United Nations on Monday expressed its alarm and called for all sides to respect the ceasefire as Israel expanded its offensive into Lebanon, while negotiations to end the U.S.-Iran war appeared in peril.

"We are deeply alarmed by the escalation in military activities across southern Lebanon and beyond," Stephane Dujarric, spokesman for U.N. Secretary-General Antonio Guterres, said.

Israeli Prime Minister Benjamin Netanyahu said on Monday he told U.S. President Donald Trump that Israel would strike Beirut if Hezbollah doesn't stop attacking Israel.

Lebanon's U.S. embassy said on Monday that Hezbollah had accepted a U.S. proposal for a "mutual cessation of attacks", after Israel threatened more strikes on south Beirut on the eve of a fourth round of Israel-Lebanon negotiations.

U.S. President Donald Trump said Monday that talks with Iran were moving ahead rapidly, despite Iran's Tasnim news agency reporting Tehran had halted talks in protest at Israel's Lebnanon offensive.

"Talks are continuing, at a rapid pace, with the Islamic Republic of Iran. Thank you for your attention to this matter!" Trump said on his Truth Social account, shortly after another post saying Israel and Hezbollah had agreed to stop attacks.

U.S. President Donald Trump said Monday he had persuaded Israel and Hezbollah to de-escalate, with Prime Minister Benjamin Netanyahu agreeing not to send warplanes to bomb Beirut's southern suburbs and the Lebanese group promising to stop attacks.

Israel said Monday it would once again target Beirut's southern suburbs, a Hezbollah stronghold mostly spared heavy attacks since April, as it stages its deepest incursion into Lebanon in two decades.