US and Iranian officials have started direct talks in Switzerland after signing an initial agreement to end the war last week, BBC reported.
The deal includes a commitment to reach a final agreement within 60 days, as well as an end to fighting on "all fronts" - including in Lebanon - and the reopening of the Strait of Hormuz.
But more clashes between Israel and Iran-backed Hezbollah in Lebanon prompted Iran to announce it had shut the shipping route on Saturday - though tracking data shows vessels have continued to pass through it.
After talks started, President Donald Trump said on social media that Iran "must immediately stop their highly paid PROXIES in Lebanon from causing trouble".
He threatened to "hit Iran very hard again" if they did not.
Before the talks began, Vice-President JD Vance had said the US hoped for progress on "the nuclear issue" and Lebanon, while Tehran said it would be "demanding that the other side fulfil its commitments".
At the Swiss resort of Bürgenstock, Vance said Trump had asked negotiators to "turn over a new leaf". He added that if Iran's leadership was willing to give up being a "driver of regional instability" and "nuclear weapons ambitions for the longer term", then the US "is willing to fundamentally transform our relationship with that country".
Iran has insisted its nuclear programme is peaceful.
Iranian foreign ministry spokesman Esmaeil Baqaei said in a statement that negotiations for a final deal were contingent on enforcing existing commitments - including stopping all military operations. Sunday's talks were focused on implementation, he said.
Vance was joined by Trump's son-in-law Jared Kushner and special envoy Steve Witkoff.
For the Iranians, parliamentary speaker Mohammad Bagher Ghalibaf and Foreign Minister Abbas Araghchi arrived in Switzerland late on Saturday.
The delegations were joined by Pakistan's Prime Minister Shehbaz Sharif and the head of the country's armed forces, Field Marshal Asim Munir.
Pakistan has acted as a mediator throughout the war, and hosted a previous round of negotiations between the US and Iran.
bd-pratidin/GR
