BEIRUT/JERUSALEM/TEHRAN - Lebanese authorities have confirmed that Hezbollah has agreed to a US proposal for a "mutual cessation of attacks" with Israel, according to a statement by the Lebanese presidency on Monday, citing the Lebanese embassy in Washington.

The statement said that the confirmation followed a phone call between Lebanese President Joseph Aoun and US Secretary of State Marco Rubio, during which the situation in Lebanon and efforts to de-escalate tensions were discussed.

According to the embassy, the US proposal calls for a reciprocal halt to attacks by both sides.

Under the proposed arrangement, Israeli strikes on Beirut's southern suburbs would cease in exchange for Hezbollah refraining from its attacks against Israel. The ceasefire framework would later be expanded to cover all of Lebanese territory.

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The embassy said that US President Donald Trump later informed Lebanon's ambassador to the United States, Nada Hamadeh Mouawad, that he had secured Israeli Prime Minister Benjamin Netanyahu's approval of the proposal.

Mouawad relayed the outcome to Aoun, who in turn informed Hezbollah of the development, the statement said.

Negotiation meetings scheduled for Tuesday and Wednesday are expected to continue building on the progress achieved, the embassy added.

Earlier on Monday, Netanyahu and Israeli Defense Minister Israel Katz said they had ordered strikes on the Beirut suburb of Dahieh, considered a Hezbollah stronghold, amid increased rocket and drone launches by Hezbollah toward Israeli military positions.

Israel eyes ‘military-controlled zone’

Katz also vowed to turn the area of southern Lebanon's Litani River into a military-controlled zone, and to continue striking Beirut until Hezbollah stops attacks.

If there is no peace in northern Israel, "there will be no peace in Beirut," Katz said in a statement released by his office.

On Sunday, Netanyahu said in a videotaped statement that he had instructed the military to deepen and expand its grip on Lebanese areas held by Hezbollah.

The instruction followed the capture of the Beaufort Ridge, including the strategic castle at its summit, in southern Lebanon by Israeli forces, an area beyond the "security zone" Israel has maintained since a ceasefire between Israel and Lebanon took effect in mid-April.

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The move, which media reports called Israel's "deepest advance into Lebanon" in over 20 years, has been met with immediate condemnation from the Arab world, as well as France, Germany and Britain.

Earlier on Monday, an Israeli soldier from an elite commando unit was killed in southern Lebanon by an explosive drone launched by Hezbollah. Three other Israeli soldiers were wounded, one of them seriously, in the village of Yohmor.

Netanyahu, Trump discuss conflict

On Monday evening, Netanyahu spoke by phone with Trump about the ongoing escalation in fighting on the Lebanese front, Israel's state-owned Kan TV News and other Israeli media outlets reported.

The reports did not detail the content of the conversation between the two leaders.

Trump said Monday night that Israel and Hezbollah have agreed to dial back hostilities following his separate calls with Netanyahu and Hezbollah representatives.

Israel's Channel 12 News quoted an Israeli senior official as saying that Hezbollah had expressed readiness in recent days for a full ceasefire without an immediate withdrawal of the Israeli army from southern Lebanon.

The channel also quoted a Lebanese senior official as saying that Lebanese Parliament Speaker Nabih Berri told the Trump administration on Sunday that Hezbollah was ready for a full and immediate ceasefire with Israel and had pledged to guarantee its implementation.

Despite the April ceasefire, Israel has continued to carry out near-daily strikes in Lebanon, while Hezbollah has launched attacks on Israeli military positions.

According to Lebanon's Public Health Emergency Operations Center, Israeli attacks since March 2 have killed more than 3,400 people and wounded over 10,200 others in Lebanon.

Iran warning

Meanwhile, Iran's main military command, Khatam al-Anbiya Central Headquarters, on Monday warned Israel against bombing Beirut and its southern district of Dahieh, the official news agency IRNA reported.

In a statement, the command warned citizens in northern Israel and military settlements in the occupied Palestinian territories to evacuate if the Israeli attacks continue.

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It accused Netanyahu of continuing his "malicious actions" in the West Asia region by threatening to bomb Beirut and Dahieh.

Also on Monday, Iranian President Masoud Pezeshkian also expressed concern over Israel's frequent ceasefire violations in Lebanon, the continued displacement of Lebanese citizens, and the US political and military support for Israel.