Mediators Pakistan and Qatar said on Monday the parties had agreed to a road map towards a final deal on ending their war in 60 days, despite a tense start as Tehran again shut the strait and US President Donald Trump threatened to resume attacks on Iran.
They said the two sides had agreed to a mechanism to end fighting between US ally Israel and Iran-aligned Hezbollah militants in Lebanon, and opened a communications line to help ensure safe passage for commercial ships through the strait, a vital global supply route for oil and liquefied natural gas.
Technical talks will continue for the rest of the week in the Qatari-owned Swiss mountain resort of Buergenstock, the joint statement said.
In a post on social media, Iranian Foreign Minister Abbas Araqchi said Tehran had secured waivers for oil and petrochemical exports, the release of some frozen assets and the launch of a reconstruction and development plan for Iran.
Oil prices rose sharply when Tehran started blockading the Strait of Hormuz, prompting a US naval blockade of Iranian ports.
But after the US and Iran signed an interim deal last week, they dropped to levels unseen since the war began on February 28 with joint US-Israeli attacks on Iran.
Oil prices fell further after Monday's joint statement, with worries about a supply shortage in global markets easing.
US Vice President JD Vance began talks with Iranian officials on Sunday under the terms of the 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.
Before talks officially began on Sunday, Fox News reported Trump had 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.
US and Iranian sources provided separate accounts of the discussions in Switzerland.
Iran's semi-official Tasnim news agency, citing an informed source, said after Trump's threats became public, the Iranian delegation refused to return to the room where talks were held, although messages were traded via the mediators.
According to Tasnim's source, Iranians said the start of negotiations on nuclear matters required the delivery of other parts of the MOU, including the release of frozen assets and US waivers authorising Iranian oil exports.
"The Iranians never left and are still here meeting and negotiating deep into the night," a US diplomat involved in the talks told Reuters.
"We've talked about the strait, Lebanon, nuclear issues, and details of implementing the MOU, among other topics."
The agreement calls for reopening the Strait of Hormuz and ending all hostilities, including in Lebanon, where Israel has continued strikes as Hezbollah fires at Israeli targets.
Iran says the US has not met a commitment to halt the war in Lebanon.
It said at the weekend it had stopped maritime traffic through the strait and that Sunday's talks would not cover substantive issues such as its nuclear program.
Vance played down the impact of violence in Lebanon at the talks, saying progress had been made towards ending hostilities there.
"These things are always a little bit messy," he said.
He told reporters Trump had "asked us to turn over a new leaf to transform our relationship with the people of Iran".
As the US lifted its maritime blockade of Iran, a second container ship docked at Shahid Rajaee port in Bandar Abbas on Monday and began loading its cargo, the director general of Hormozgan Ports and Maritime Organisation said.
Despite the announcement of a new ceasefire in Lebanon on Friday, there has been scant sign of an end to fighting there.
Iran said on Saturday that as a result, it had again shut the strait.
Israeli President Isaac Herzog said on Monday Israel was not opposed to a diplomatic end to the Iran war, but any agreement must ensure Tehran cannot use funds it receives as part of the deal for military purposes or to support regional proxies.
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