Iranian negotiators have suspended high-stakes talks with the US in Switzerland in protest at a stream of threats issued by Trump to bomb Iran, and even to kidnap the Iranian negotiating team unless the strait of Hormuz is reopened.

It was not clear if the Iran walkout was permanent or a symbolic show of protest. But before leaving the face-to-face talks in Burgenstock, Iran reached a draft agreement over how the US will issue a waiver lifting sanctions on Iranian oil exports, one of the key preconditions before Iran will open talks on its nuclear file.

Iranian officials claimed the waivers would be issued soon, adding progress had also been made on unfreezing Iranian assets in overseas bank accounts

Iran and the US last week signed a memorandum of understanding designed to lift the blockade on the strait of Hormuz, leading to 60 days of talks on Iran’s civil nuclear programme.

Trump’s stream of aggressive threats on social media and in TV interviews filtered across the Atlantic to the negotiating site, causing anger among the Iranian negotiating team, who said they represented an unacceptable threat to their personal safety. They pointed out the memorandum signed by Trump last week included a non-aggression pact.

Trump’s threats contrasted with the tone adopted by his vice-president, JD Vance, who said he had been asked by the president to use the talks to turn over a new leaf with Iran.

Iran’s chief negotiator, Mohammad Bagher Ghalibaf, said: “Don’t they think to themselves that if their threats had any effect, they wouldn’t have reached the desperation they face today? We don’t take the Americans’ threats into account at all.”

But the delegation felt compelled to walk out in protest partly because there is domestic political pressure on the negotiators to show they distrust the Trump negotiating team.

Iran said it had remounted its blockade in the strait of Hormuz in protest at the continued Israeli attacks in Lebanon and said Trump was allowing Israel to breach the memorandum of understanding signed by the US president and his Iranian counterpart, Masoud Pezeshkian, last week. The memorandum clearly calls for a ceasefire on all fronts, but Israel killed more than 30 people in attacks on Saturday in central and southern Lebanon.

“Iran must immediately stop their highly paid proxies in Lebanon from causing trouble,” Trump wrote on social media. “If they don’t, we’ll hit Iran very hard again.”

In a 20-minute phone call with Fox News, which revealed his sensitivity to the criticism being directed at him by Republicans and Democrats alike, he said: “We may take over the strait, if we have to. If they don’t make a deal, we’ll collect tolls.”

Referring to the strait, he appeared to threaten to kidnap the Iranian negotiators, 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’s threat led to a formal protest by the Iranians to the mediators, and a demand that what they described as his “bullying” was brought under control.

At the talks in Switzerland, 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.

Adopting a contrastingly emollient tone to Trump, he added: “What the president has asked us to do, is turn over a new leaf, to transform our relationship with the people of Iran and to extend an outstretched hand, that says to the people of Iran that if your leadership is willing to give up being a driver of regional instability, if they are willing to give up nuclear weapons ambitions for the long term, then the United States is ready to fundamentally transform our relationship with that country.

“The question before us now is how much more can we accomplish together? Can we turn over a new leaf?”

The US energy secretary, Chris Wright, said the renewed Iranian blockade was having no effect and claimed that 67 ships had transited the waterway on Saturday, on top of 55 ships on Friday.

The practical impact of the Iranian decision to keep the strait closed is yet to be tested, but Trump said last week that the world was four weeks from running out of sufficient refined oil, and said there would have been a worldwide recession if he had not agreed to the strait’s reopening by lifting the US blockade on Iranian oil ports.

The Republican senator Lindsey Graham, a close confidant of Trump, said: “I spent four and a half hours with President Trump on Friday. Here’s what I think will happen next. If this deal fails, President Trump is going to take the strait of Hormuz over by force … We’ll charge a fee for all those who go through to pay for the operation … if Iran contests control of the strait of Hormuz by the United States we’ll obliterate them.”

Trump is under fierce attack from US supporters of Israel who are angry at the personal attacks mounted on the Israeli prime minister, Benjamin Netanyahu, by Trump and Vance.

Speaking at a memorial service for his late brother, Yonatan, Netanyahu said Israel would “remain in the security buffer zone in southern Lebanon for as long as necessary”, a reference to an area up to 6 miles from the border that Israel has occupied. Netanyahu also reiterated his claim that he “will not allow Iran to arm itself with nuclear weapons”.

Iran says the talks must focus on the Lebanon ceasefire, the terms for the reopening of the strait, and the lifting of US sanctions on Iranian oil exports, alongside the unfreezing of Iranian assets held abroad. The head of the Iranian delegation, Mohammad Bagher Ghalibaf, has brought with him the CEO of the National Iranian Oil company, and the head of Iran’s central bank, suggesting that the technicalities of oil sanctions being lifted and the channels through which frozen money can be directed to Iran are at the forefront of Iranian thinking.

The Iranian delegation refused to appear on camera alongside the US delegation led by Vance, Trump’s son-in-law Jared Kushner and the US special envoy Steve Witkoff. But the two delegations were briefly filmed in the same room, and the format of the afternoon talks involved Iran, the US, Pakistan and Qatar in a quadrilateral format. Qatar is deeply entrenched as the joint mediator alongside Pakistan.

The head of the UN nuclear watchdog, Rafael Grossi, was also in Switzerland, but the Iranian delegation want to postpone talks on the future inspections of its nuclear sites until after the sanctions disputes are resolved. The aim is to resolve the nuclear issues, including the intrusiveness and frequency of IAEA inspections within 60 days, but the period can be extended by mutual agreement.