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.

Iran's Tasnim news agency said Tehran was suspending all exchanges with mediators in peace talks with the United States on Monday, blaming Israel's ongoing invasion of Lebanon.

"Given the continuing crimes of the Zionist regime (Israel) in Lebanon and considering that Lebanon was one of the preconditions for the ceasefire and that this ceasefire has now been violated on all fronts, including Lebanon, the Iranian negotiating team is suspending dialogues and exchange of texts through mediators," Tasnim reported.

Hezbollah said its fighters were still battling Israeli troops near south Lebanon's Beaufort castle on Monday, a day after Israel said it seized the strategic fortress and troops raised the Israeli flag there.

The European Union on Monday urged Israel to halt its military operation in Lebanon, after Israel seized the strategic Beaufort Castle and said it would resume strikes on southern Beirut.

"We call on Israel to stop its military escalation in Lebanon and to respect Lebanon's sovereignty and territorial integrity," EU spokesman Anouar El Anouni said.

Iranian Foreign Minister Abbas Araghchi said Monday that attacking Lebanon violates the ceasefire "on all fronts," warning that "the U.S. and Israel are responsible for the consequences of any violation," after Israeli officials threatened to bomb Beirut's southern suburbs.

"The ceasefire between Iran and the US is unequivocally a ceasefire on all fronts, including in Lebanon. Its violation on one front is a violation of the ceasefire on all fronts. The US and Israel are responsible for the consequences of any violation," Araghchi wrote on X.

France's President Emmanuel Macron said on Monday he had encouraged his US counterpart Donald Trump to pursue his "determined efforts" to reach a ceasefire deal with Iran to end the Middle East war.

Israel's defense minister said Monday there would be "no calm in Beirut" if Hezbollah attacks continued and vowed to establish a military-controlled zone in the area of south Lebanon's Litani River.

"The Dahieh in Beirut is no different from the communities in northern Israel -- if there is no calm in the north, there will be no calm in Beirut," Israel Katz said in a statement released by his office, referring to the Beirut southern suburb and Hezbollah stronghold where he had earlier Monday ordered strikes.