“Positive and constructive” talks between the US and Iran in Switzerland have wound up after ‌a tense opening marked by Tehran’s announcement it had again closed the Strait of Hormuz and US President Donald Trump repeating his threats of more attacks on Iran.

A joint statement on Monday from mediating nations Qatar and Pakistan said the US and Iran agreed to a roadmap toward a final ‌peace deal within 60 days.

Technical talks will continue for the rest of the week in the Qatari-owned Swiss mountain resort of Buergenstock, according to the statement, which was released by the Qatari foreign ministry.

It said there had been agreement on a mechanism to end the fighting in Lebanon and a communications line had been opened to help ‌ensure safe passages for commercial ships through the contested strait.

US Vice President JD Vance opened 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 early on Monday (local time).

In a post on social media, Iranian Foreign Minister Abbas Araqchi said his country 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.

Just before talks officially began on Sunday, Fox News reported that Trump had told Iranian officials “you won’t have a country” if they tried to close the strait again. He also reiterated an earlier threat that the US would ‌take over the waterway and possibly ‌charge a toll of its own.

According to state media Tasnim, foreign ministry spokesperson Esmaeil Baghaei said Iran initially refused to continue the talks after Trump’s threats.

“During the four-party meeting [mediated by Qatar and Pakistan], a threatening statement from the United States was published, which led Iran to announce that under such circumstances it was not willing to continue the four-way talks, Baghaei said.

Qatar and Pakistan later released a statement saying “encouraging” progress was made by both sides.

“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.”

A senior US diplomat engaged in the talks said the Iranians had remained in the talks, and much of the discussions had included clarifying what Iran meant by some of its recent statements about the Strait of Hormuz.

The negotiators also discussed various “mechanisms” to ensure the strait remains open and that a ceasefire in southern Lebanon is enforced.

Iran, arguing that the US had failed to meet its commitment to halt fighting in Lebanon, said on the weekend that it had again stopped maritime ‌traffic through the Strait of Hormuz and that Sunday’s talks ​would not cover substantive issues such as Iran’s nuclear program.

In Switzerland, where US and Iranian officials met along with Qatari mediators, Vance played down the impact of violence in Lebanon, saying there had been progress towards ending hostilities there.

“These things are always ​a little bit messy,” ‌he said.

On social media Trump threatened to resume attacks on Iran if it did not rein in its allies.

“Iran must immediately stop their highly paid PROXIES in Lebanon from causing trouble,” he wrote, apparently referring to Hezbollah.

“If they don’t, ​we’ll hit Iran very hard again, just like we did last week, only harder!!!”

He also told Fox News he had issued a warning to Iran, after Tehran said on Saturday it would not open the Strait of Hormuz, citing ongoing Israeli attacks on Lebanon.

“You close it and you won’t have a country,” Trump was quoted as saying.

“You won’t even make it back to your f—ing country.”

Even as Trump was threatening Iran, Vance said he had “asked us to turn over a new leaf to transform our relationship with the people of Iran”.

A US diplomat 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”.

Despite the announcement of a 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, whose closure for nearly four months caused the biggest disruption of global energy supplies in history.

US officials ‌dispute that the strait was closed, but commercially available shipping data showed an immediate impact.

Five vessels passed the strait on Sunday, a sharp drop from the 26 ships spotted a day earlier, data from analytics firm Kpler showed. The data may exclude vessels that switch off their transponders while travelling in the Gulf.

Iran’s Fars news agency cited a military source as saying on Sunday that no permits were being issued for ships to cross.

-with AAP