Iran’s foreign minister has declared “progress” after the first day of talks between high-ranking officials from Washington and Tehran ended in Switzerland, despite a tense opening marked by Donald Trump threats to restart attacks.

A joint statement from mediators Qatar and Pakistan said the ⁠US and Iran agreed to a roadmap towards⁠ a final deal within 60 days. Technical talks between lower-ranked officials ​will continue for the rest of the week, according to the statement, with fighting between Israel and Iran-backed Hezbollah in Lebanon at the top of the agenda.

“Pakistani and Qatari mediation has delivered major progress to end Lebanon war,” said Abbas Araghchi, the Iranian foreign minister, after talks broke up just after 3am local time (1am GMT).

The joint statement said the US and Iran agreed to establish a “communication line” to avoid incidents in the strait of Hormuz, and to set up a “de-confliction cell” with Lebanon’s government to ensure the “adherence of the termination of military operations in Lebanon”.

In a development that is critical to unlocking progress, the US Treasury was also preparing to issue a 60-day waiver lifting sanctions on oil, petrochemicals and derivatives. Iran said this meant its central bank would be able to sell oil to customers, principally China, and receive payments without the threat of sanctions.

Qatar and Iran also signed a memorandum about the release of Iranian assets frozen in Qatar bank accounts due to US secondary sanctions. It was not clear whether the US had placed any restrictions on Iran’s use of the assets, such as demanding the money only be spent on humanitarian goods.

The economic measures may help lift some of the pressure in Iran’s exchange markets, and gradually slow runaway inflation, the country’s biggest domestic concern at present.

The joint statement by the mediators focused on new implementation mechanisms to turn the memorandum of understanding (MOU) signed last week by Washington and Tehran into reality over the next 60 days – the timeline set out to reach an agreement on the future of Iran’s nuclear programme and the lifting of sanctions on its economy.

Although the main talks involving the US vice-president, JD Vance, and the Iranian chief negotiator, Mohammad Bagher Ghalibaf, were declared concluded, lower-ranked officials will remain in the Swiss resort of Bürgenstock to continue the technical discussions.

In his message, Araghchi said the first real test of the understandings reached would be this “deconfliction” method for Lebanon, which has emerged as the biggest threat to the agreement signed by the US and Iran last week.

Over the weekend, Iran said it had reinstated its blockade in the strait of Hormuz in protest at the continued Israeli strikes on Lebanon and that Trump was allowing Israel to breach the MOU. The memorandum calls for a ceasefire on all fronts, but Israel killed more than 30 people in attacks on Saturday in central and southern Lebanon.

Despite the US military denying that the strait had been closed, Trump responded strongly to the threat on Sunday, saying: “You close it and you won’t have a country. You won’t even make it back to your fucking country.”

The US president also weighed in on the situation in Lebanon, writing on social media: “Iran must immediately stop their highly paid proxies in Lebanon from causing trouble … If they don’t, we’ll hit Iran very hard again.”

Iranian state media said talks had paused after the “publication of an insulting message by the US President”. The Iranian delegation then met with Qatari mediators and left the negotiating site, state media said. Iran’s semi-official Tasnim news agency said the Iranian delegation refused to return to the room where talks were held, but messages were still being traded via Pakistani and Qatari mediators.

Speaking to reporters, a senior US diplomat said late on Sunday that the Iranians remained on site and the negotiations were on, according to the Associated Press.

Vance was joined by US special envoy Steve Witkoff and the president’s son-in-law, Jared Kushner. Iran was represented by Ghalibaf, Iran’s parliamentary speaker, and Araghchi. It was unclear whether Vance was set to continue the talks on Monday. The vice-president told US media that he anticipated staying only a “day or two”.

“The question before us now is how much more can we accomplish together? Can we turn over a new leaf?” Vance said as the talks began.

Vance and his US negotiating team will use the 60 days of talks to try to reach an agreement over Iran’s nuclear programme. The MOU calls for Iran to, at minimum, dilute its stockpile of highly enriched uranium, but many issues – including Tehran’s right to enrich uranium in the future – remain unresolved.

Iran had sought to hold back the nuclear element of the talks until the US blockade of its oil ports was lifted, a clear oil sales sanctions waiver was published, and half of its estimated $24bn in overseas assets were unfrozen and returned to Tehran.

But with the bulk of its preconditions met, the joint mediator’s statement indicated that Iran would now permit some talks to take place on the future of its domestic uranium enrichment and the downblending of its large stockpile of highly enriched uranium.

Araghchi acknowledged the most difficult issue remained the future of the Lebanon crisis describing “the elimination of the conflict in Lebanon as the first real test” of the agreement.