The first round of talks between high-ranking US and Iranian officials in Switzerland have ended on Monday, mediators said.
A joint statement from the mediating nations, Qatar and Pakistan, said that the US and Iran agreed to a roadmap toward a final deal within 60 days.
Technical talks will continue for the rest of the week at the Qatari-owned Swiss mountain resort of Bürgenstock, according to the statement released by the Qatari foreign ministry.
The parties agreed to a mechanism to end the fighting in Lebanon and opened a communications line to help ensure safe passages for commercial ships through the contested strait, the statement said.
US Vice President JD Vance began talks with Iranian officials on Sunday under the terms of a memorandum of understanding reached last week to extend a tenuous ceasefire from April for at least another 60 days. The discussions continued until the early hours of Monday.
The White House had no immediate comment when asked if high-level talks had wrapped for now.
Just before talks officially began on Sunday, Fox News reported that Trump said he told Iranian officials "you won't have a country" if they tried to close the Strait again.
Trump also reiterated an earlier threat that the US would take over the waterway and possibly charge a toll of its own, Fox News said.
Trump said he agreed to last week's memorandum of understanding to avert a global economic depression from high oil prices caused by the strait's closure. Oil prices had tumbled over the past week to levels unseen since the war started on February 28 with US-Israeli attacks on Iran.
After the joint statement, Brent crude futures fell further, dropping more than $1 to $79.44 a barrel.
The agreement calls for reopening the Strait of Hormuz, a choke point for global energy shipments, and ending all hostilities, including in Lebanon, where Israel has continued to launch deadly strikes as Hezbollah fires at Israeli targets.
At the talks in Switzerland, where US and Iranian officials met in the presence of Qatari mediators, Vance played down the impact of violence in Lebanon, saying progress had been made towards ending hostilities there. "These things are always a little bit messy," he said.
Back in the United States, Trump threatened to resume attacks on Iran if it did not rein in its allies.
Even as Trump was threatening Iran, Vance told reporters the US president had "asked us to turn over a new leaf to transform our relationship with the people of Iran."
A US diplomat late Sunday said discussions included “clarifying some of the confusing messaging from Iran on the Strait and building deconfliction mechanisms to ensure the Strait will remain fully open.”

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