Top-level talks were due to start in the Swiss mountain resort of Bürgenstock on Sunday between US Vice President JD Vance and Iranian representatives along with Pakistani and Qatari mediators.
The talks were overshadowed by reports of further clashes between Israeli forces and the Hezbollah militia in Lebanon despite the ceasefire in the conflict.
Under the terms of the ceasefire between Washington and Tehran, a final agreement is to be reached within 60 days on Iran's nuclear programme.
However, the ceasefire already appears to be vulnerable, with Iran's military announced on Saturday it was again closing the Strait of Hormuz to all shipping in response to the ceasefire violations in Lebanon.
Trump meanwhile threatened to impose a US-controlled transit fee in key waterway if a deal is not achieved within the 60-day timeframe.
Ahead of Vance's departure, he told reporters: "I think we're going to hopefully make progress on the nuclear issue, make progress on the Lebanon ceasefire issue."
He added that US special envoy Steve Witkoff and Trump's son-in-law Jared Kushner were already in Switzerland and that he expected to spend at most two days in the country.
The Iranian delegation is expected to include Parliament Speaker Mohammad Bagher Ghalibaf and Foreign Minister Abbas Araghchi. Pakistani Prime Minister Shehbaz Sharif is also to be present.
An initial round of talks was scheduled for Friday but was called off after renewed clashes in Lebanon.
