Burgenstock, Switzerland - Iran's chief negotiator, Mohammad Bagher Ghalibaf, and Foreign Minister Abbas Araghchi have left Switzerland following 18 hours of intensive talks with US representatives, the Iranian news agency Tasnim reported on Monday morning.

Iran and the US agreed Monday to set up communications lines to keep the vital Strait of Hormuz open and end fighting in Lebanon, mediators said, after their first round of talks in Switzerland toward ending the war in the Middle East.

The teams led by US Vice President JD Vance and Iran's Mohammad Bagher Ghalibaf opened talks Sunday, as part of a two-month negotiating period set out under a preliminary deal agreed last week.

Mediators Pakistan and Qatar said the negotiators reached agreement on a "roadmap towards reaching a final deal within 60 days," with technical talks to continue for the rest of the week at the Swiss resort of Burgenstock.

In a statement, the mediators said negotiations would continue in smaller working groups later in the week.

"Encouraging progress has been made including the creation of a mechanism for further technical talks," they said, detailing a contact channel set up to "avoid incidents and miscommunication" at the Strait of Hormuz.

A "de-confliction cell" between the parties and the Lebanese authorities has also been agreed to prevent fighting from erupting again, they said.

Tehran had effectively closed the Strait of Hormuz in retaliation against the joint attacks by Israel and the US on February 28 that touched off the war in the Middle East.

After a series of false starts, Washington and Tehran finally signed last week a memorandum of understanding towards ending the conflict that included a provision to end fighting in Lebanon. The overall death toll in Lebanon has surpassed 4,100 people since Israel launched its assault on March 2, the health ministry said.

Israel has continued to attack Lebanon since, which prompted Iran to say it would again shutter Hormuz through which oil and gas shipments transit, having opened it as part of the deal.

"Tireless Pakistani and Qatari mediation has delivered major progress to end Lebanon War," Iran's Foreign Minister Abbas Araghchi wrote on X after the high-level talks in Switzerland.

"Oil and petrochem exports are waived, blockade lifted, some frozen assets released, and major reconstruction & development plan launched for Iran. 1st real test: Lebanon deconfliction cell," he wrote.

There was no immediate reaction from US negotiators, but crude prices slipped while stocks mostly gained in Asia as the progress reported by mediators fueled optimism.

The development came after a shaky start to the negotiations, with the Islamic Republic's delegation walking out in response to President Donald Trump's threats to strike Iran over its support for Hezbollah Sunday.

Iran hit back with a warning of its own.

"They would do better to be careful with their statements; our armed forces are ready to respond to them in a different manner. No matter what they say, we are the ones who act," Iran's chief negotiator Mohammad Bagher Ghalibaf said.

Israeli Prime Minister Benjamin Netanyahu, meanwhile, said troops would remain in south Lebanon "as long as necessary" and vowed that he would "not allow Iran to acquire nuclear weapons."

Vance had earlier hailed "a historic meeting" in Switzerland.

Flanked by US negotiators Jared Kushner and Steve Witkoff, Vance added: "The question before us now is how much more can we accomplish together?

"Can we turn over a new leaf? Can we change relations in the Middle East permanently?"

"Or do we go back to doing things the old way, which is not our preference, but it's certainly very much something that can happen."

Speaking on Sunday, Iranian President Masoud Pezeshkian underlined Tehran would not relinquish its right to enrich uranium, though he repeated Iran's denial that it wants nuclear weapons.

"We can also state in writing that we have no intention of building a bomb," he said.