The first round of negotiations between the US and Iran to reach a final deal to end the war has ended with "encouraging progress", mediators Qatar and Pakistan say.

In a joint statement early on Monday, Qatar and Pakistan said that the parties had agreed to "a roadmap towards reaching a final deal within 60 days".

Iran's foreign minister Seyed Abbas Araghchi said there had been "major progress" towards ending the conflict in Lebanon.

The memorandum of understanding (MoU) signed last week includes a commitment to ending the fighting on "all fronts" - including Lebanon - and the reopening of the Strait of Hormuz.

"Pakistani and Qatari mediation has delivered major progress to end Lebanon War," Araghchi posted on social media.

"Oil and petrochem exports are waived, blockade lifted, some frozen assets released, and major reconstruction & development plan launched for Iran."

The Iranian lead negotiators left the talks in Switzerland on Monday, Iranian media said, with technical discussions between the parties due to continue.

The mediators' joint statement said that a "communication line" had been formed "to avoid incidents and miscommunication with the aim of safe passage for commercial vessels through the Strait of Hormuz".

Both sides also agreed to the creation of a "de-confliction cell" between the US, Iran and Lebanon, facilitated by the mediating countries, to end military operations in Lebanon, their statement said.

Araghchi said the first "real test" would be the Lebanon de-confliction cell.

Lebanese President Joseph Aoun spoke to senior officials from the US and Qatar on Monday about the issue, and more broadly about consolidating a ceasefire in Lebanon, his office said.

Since the MoU was signed, there has been an upsurge in fighting between Lebanese armed group Hezbollah and Israeli forces in southern Lebanon, and Israeli air strikes that the health ministry says have killed dozens of Lebanese including women and children.

A new ceasefire between Israel and Hezbollah was declared on Friday.Continued clashes and air strikes prompted Iran on Saturday to announce it had shut the Strait of Hormuz, though tracking data shows vessels have continued to pass through it.

Hezbollah said it was committed to the ceasefire but that it would confront any attempt by Israel to "seize territory or expand its occupation".

The group said its fighters had clashed with Israeli forces advancing towards the Ali al-Taher hill area, which is on the edge of the southern village of Kfar Tebnit and overlooks the major town of Nabatieh in the south.

The Israeli military's chief of staff said on Sunday that Hezbollah had built an "underground military fortress" beneath the hill and that its destruction was one of the "primary operational focuses" of Israeli forces.

Fighting was reported to have diminished on Sunday but Israeli Prime Minister Benjamin Netanyahu insisted that the Israeli military would remain in southern Lebanon for as long as was necessary to protect northern Israel.

Speaking before the talks at the Swiss resort of Bürgenstock, US lead negotiator Vice-President JD Vance said Trump had asked negotiators to "turn over a new leaf".

He added that if Iran's leadership was willing to give up being a "driver of regional instability" and its "nuclear weapons ambitions for the longer term", then the US "is willing to fundamentally transform our relationship with that country".

Iran has insisted its nuclear programme is peaceful.

Under the initial deal signed last week, Iran was to reopen the Strait of Hormuz, the key shipping channel through which 20% of the world's oil and natural gas travels.

The US also agreed to lift a military blockade on ships going to and from Iranian ports.

The deal also includes a $300bn (£224bn) plan for Iran's "reconstruction", and the US terminating "all types of sanctions" on it.

But the issue of Iran's nuclear programme is still to be negotiated.

On Sunday some vessels appeared to be entering, exiting and transiting the strait, according to location data on the maritime tracking website MarineTraffic, despite Iran's claim - disputed by the US - to have closed the strait.

The initial deal also called for fighting to stop on all fronts,but in Lebanon Israeli air strikes have since killed at least 67 people, while Hezbollah attacks have killed five Israeli soldiers.

Israel has insisted that its conflict with Hezbollah is separate from the war on Iran, which it mounted alongside the US on 28 February.

Lebanon was drawn into the war shortly afterwards, when Iran-backed Hezbollah launched rockets into Israel in retaliation for a strike that killed Iran's supreme leader.

Israel responded by launching a bombing campaign across Lebanon and occupying around 5% of the country's territory in the south - hoping to drive back Hezbollah fighters from its northern border - and has said it has no intention of withdrawing.

Since 2 March, at least 4,106 people have been killed in Lebanon, the country's health ministry says. Its figures do not differentiate between combatants and civilians.

Israeli authorities say 36 Israeli soldiers and four civilians have been killed on both sides of the border.