The Lebanese presidency said Aoun thanked Rubio for US support but stressed "the need for Israeli attacks on Lebanese territory to cease through the achievement of a comprehensive ceasefire".
Rubio, according to the US State Department, insisted on the importance of Lebanon carrying through on its efforts to disarm the Hezbollah armed group, which is fighting Israel in the south of the country.
"They discussed the next round of negotiations, scheduled for June 23 to 25 in Washington, where the two sovereign governments will make progress toward a lasting peace," a spokesman said. "Secretary Rubio reiterated the need to disarm Hezbollah and to re-establish control over all Lebanese territory."
Israel's ambassador to the United States, Yechiel Leiter, insisted in a social media post that Israel was committed to an immediate ceasefire in Lebanon, but only "if Hezbollah honours the agreement and ceases its hostilities".
The deal signed this week by President Donald Trump and his Iranian counterpart Masoud Pezeshkian aims to end a war that began on February 28 with US-Israeli strikes that killed supreme leader Ayatollah Ali Khamenei.
The agreement was also meant to halt the fighting in Lebanon, which Iran has always insisted should be covered under any accord, turning Israel's ongoing campaign there into a source of frustration for Washington.
Israel's military said Friday that it had struck more than 80 Hezbollah targets in Lebanon and killed dozens of members of the Iran-backed group.
'Permanent war'
But a US official told AFP a truce between Israel and Hezbollah, beginning immediately, had been brokered by US and Qatari mediators following talks with Israel and Iran. A Gulf diplomat confirmed the ceasefire.
Even after the truce was announced, Lebanese state media reported an Israeli airstrike on the country's south in the Jezzine region.
Leiter, however, denied this, saying: "At 11:30 this morning, Israel halted all offensive operations; Hezbollah and Iranian claims to the contrary are bold lies."
A previous truce nominally agreed in April did nothing to stop attacks by either side, and Prime Minister Benjamin Netanyahu had said just hours earlier that the Israeli army would make Iran-backed Hezbollah pay a "heavy price" for its attacks.
Far-right Israeli National Security Minister Itamar Ben Gvir went even further, saying after the soldiers' deaths that "all of Lebanon must burn".
Iran's Foreign Minister Abbas Araghchi accused Israel of only being interested in "permanent war".
