JD Vance said on Monday that Iran has agreed to allow nuclear inspectors into the country again following an initial round of discussions aimed at resolving the conflict with the United States.Speaking after discussions in Switzerland, the US vice president said the development was “probably what we’re most excited about as Americans”, and that plans could be drawn up as soon as this week.Iran’s nuclear programme has been at the centre of the dispute with the US and Israel since before the conflict erupted, and remains the focus of the new 60-day window for talks to finalise a deal to end the war.“That is a major milestone for the American people, and the first step in permanently denuclearising or permanently ending a nuclear weapons program in Iran, and that’s exactly what we wanted to do,” Vance said.Vice president JD Vance hailed progress in the recent talks with Iran (Getty)The International Atomic Energy Agency (IAEA) serves to promote the peaceful use of nuclear energy, and is mandated to monitor facilities, report on activities, oversee safety and promote peace through diplomacy.It halted its inspections of Iranian facilities in February, after the war started, and has not been back since. Iran suspended its cooperation with the watchdog last year following US-Israeli strikes on its facilities.In a sign of tentative progress, Vance also revealed on Monday that the parties had agreed on a mechanism to keep the Strait of Hormuz open and ensure a regional ceasefire, after the parallel conflict in Lebanon threatened to derail the peace process on Friday.“As the President of the United States has himself said, sometimes these ceasefires just mean you’re shooting a little bit less,” he said.“But we wanted to make sure that we had the proper coordination set up so that if there is shooting, if Hezbollah fires at Israel or if Israel responds, if there are other conflicts that arise in the region, we’re actually talking to each other and figuring out how to stop the shooting.”Vance said that Trump urged him to “turn over a new leaf” with Iran, despite the president’s threats over the weekend to “take over” the country if the regime closed the Strait of Hormuz again.He played down the recent rhetoric, saying: “There was a little bit of threatening, there was a little bit of whining, but at the end of the day the talks continued and we made great progress.”The status of the Strait of Hormuz remained in focus on Monday, Vance said (as seen from Oman on 18 June) (Reuters)Trump’s comments had drawn backlash from Iranian officials earlier on Monday.Ebrahim Azizi, the head of the Iranian parliament’s national security and foreign policy commission, said that Iran would take action where the US makes threats, adding that the Strait “is neither your personal casino not the backyard of modern-day pirates”.”These are Iranian sovereign waters, and the ultimate decision rests with the noble people of Iran and its brave armed forces,” he said, amid questions over the future of the waterway and Iran’s threats to impose fees on transit.Despite an outburst of rhetoric on both sides, negotiators and mediators joined Vance in hailing progress. In a move suggesting the US was upholding its end of the initial agreement, the treasury department on Monday authorised the production, delivery and sale of Iranian oil through until 21 August.The main Iranian negotiating team, including senior diplomat Mohammad Baqer Ghalibaf, left Switzerland for Tehran on Monday, but technical talks were expected to continue for the rest of the week.The president of Iran, Masoud Pezeshkian, was also expected to travel to Pakistan, mediating the talks, on Tuesday to discuss “ongoing diplomatic engagements”, the Pakistani government said.A man with a Hezbollah flag drives past a damaged building in Nabatiyeh, southern Lebanon, which has been devastated by Israeli airstrikes (AP)Oil prices fell some 0.7 per cent amid growing optimism that an end to the conflict could be insight. Still, only a handful of vessels were reported to have crossed the Strait of Hormuz on Monday, after Iran’s Revolutionary Guards declared the waterway shut on Saturday.A tenuous ceasefire in Lebanon appeared to hold on Monday, as security sources reported that Israel had not carried out an airstrike since Saturday evening. They said the lull in violence was the longest since Hezbollah opened fire in support of Iran on March 2, although an Israeli drone could be heard over Beirut.Israeli President Isaac Herzog said 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.Donald Trump continued to threaten Iran and face criticism at home over the war (AFP/Getty)Trump meanwhile was still facing criticism over the shape of the initial memorandum of understanding (MoU) intended as a framework from which to begin talks.The president on Sunday attacked the New York Times over a report asking what the war had actually achieved.He wrote on Truth Social: “The way the Corrupt and Failing New York Times is covering stories on a very battered and beat up Iran, through FAKE & MADE UP ‘FACTS’ is, in my opinion, ‘TREASONOUS,’”.“I will be adding all of their false and ridiculous reporting to my multi Billion Dollar lawsuit against them. They are Criminals!” he said.