JD Vance says Iran has agreed to allow nuclear inspectors back into the country - a key demand of the international community - with discussions with the International Atomic Energy Agency (IAEA) happening "as soon as today".
The US vice-president said a great deal of progress had been made after the first round of talks between the US and Iran to reach a final deal to end the war, echoing a statement by mediators.
He said teams had discussed the reopening of the Strait of Hormuz and "de-confliction for the regional ceasefire".
The memorandum of understanding (MOU) signed last week includes a commitment to re-opening the strait and the ending the fighting on "all fronts" - including Lebanon.
In a joint statement released earlier on Monday, mediators Qatar and Pakistan said that after the first round of talks, the US and Iran had agreed to "a roadmap towards reaching a final deal within 60 days". Vance described the talks as having laid a "very good foundation" for negotiations towards a final settlement.
Speaking in Switzerland on Monday morning, the vice-president said the nuclear issue was "probably the one we're most excited about as Americans".
"[This] is a major milestone for the American people and a first step in permanently... ending a nuclear weapons programme in Iran," he said.
Iran has always insisted that its nuclear programme is for civilian purposes only.
Asked by reporters when nuclear inspectors from the UN's nuclear watchdog would be returning to Iran, Vance said he expected the process to start "at a minimum this week", but conversations with inspectors and the IAEA "could happen as soon as today".
The 14-point MOU, signed last week by US President Donald Trump and his Iranian counterpart Masoud Pezeshkian, references to the IAEA, specifically on addressing the country's stockpile of enriched nuclear material.
Tehran says it is not trying to develop nuclear weapons, but many countries - as well as the global nuclear watchdog, IAEA have been not convinced.
In 2015, Iran and six world powers – the US, China, France, Russia, Germany and the UK – agreed to a nuclear deal known as the Joint Comprehensive Plan of Action (JCPOA) after years of negotiations.
As well as limiting what Iran was permitted to do with its nuclear programme, it allowed the IAEA to access all of Iran's nuclear facilities and to carry out inspections of suspect sites.
During Donald Trump's first term, in 2018, he removed the US – which had been a key pillar of the agreement, arguing it was a "bad deal" because it was not permanent and did not address Iran's ballistic missile programme, amongst other things.
Iran suspended IAEA access to sites bombed by Israel and the US during the 12-day war in June 2025. The following month, the UN's nuclear watchdog said it had pulled out its remaining inspectors from the country.
The Iranian lead negotiators left the talks in the Swiss resort of Bürgenstock on Monday, Iranian media said, with technical discussions between the parties due to continue.
The mediators' joint statement said that a "communication line" had been formed "to avoid incidents and miscommunication with the aim of safe passage for commercial vessels through the Strait of Hormuz".
Both sides also agreed to the creation of a "de-confliction cell" between the US, Iran and Lebanon, facilitated by the mediating countries, to end military operations in Lebanon, their statement said.
Iran's Foreign Minister Seyed Abbas Araghchi said the first "real test" would be the Lebanon de-confliction cell.
The initial deal also called for fighting to stop on all fronts, but in Lebanon Israeli air strikes have since killed at least 67 people, while attacks by Lebanese armed group Hezbollah have killed five Israeli soldiers.
