A high-level Iranian team arrived in Switzerland for peace talks with the US, Iranian state media reported, and Vance touched down at Emmen Air Base at 6am on Sunday (2pm AEST) for meetings in the mountain town of Burgenstock, overlooking Lake Lucerne.
Although the US and Iran had agreed to a 60-day ceasefire while negotiations take place, Tehran's Islamic Revolutionary Guard Corps on Saturday declared the Strait of Hormuz shut, though the US military said commercial vessels continued operating in the waterway.
Those developments could complicate talks in which both sides seek to advance an interim deal brokered by Pakistan and signed on Wednesday by US President Donald Trump and Iranian President Masoud Pezeshkian to end their almost four-month war.
Pointing to what it called Israeli "crimes" in Lebanon that violated US commitments to a ceasefire, the IRGC warned ships would be at risk if they approached the Strait, a vital conduit for global oil and gas supplies.
But US Central Command said 55 merchant ships transited the strait on Saturday, with more than 17 million barrels of oil.
US forces will ensure commercial traffic continues, Central Command added.
Trump in a social media post on Saturday wrote that no toll would be charged for passage through the Strait during or after the 60-day ceasefire - unless the US imposed one should peace talks fail.
Trump left open the possibility of a Hormuz toll levied by the United States "for services rendered as the Guardian Angel to the countries of the Middle East" if a peace deal wasn't sealed.
Mohammad Mokhber, an adviser to Iranian Supreme Leader Ayatollah Mojtaba Khamenei, accused the US on X of failing to implement the first clause of its 14-point interim deal with Iran, which includes a ceasefire "on all fronts", including Lebanon.
As long as the agreement was only on paper, the flow of Middle East energy would remain halted, he said.
The Lebanon truce appeared fragile as Israeli forces and the Iran-backed militant group Hezbollah attacked each other.
Iranian Foreign Ministry spokesperson Esmaeil Baghaei said Iran would press in Switzerland for fulfilment of commitments, citing past failures by the other side to honour agreements.
Vance, in an interview with Fox News, said he was confident the ceasefire would hold, and he had seen no evidence that the Strait of Hormuz was closed.
Negotiators would likely have a "couple days of talks", Vance told reporters before boarding a plane at Joint Base Andrews in Maryland.
"I think we're going to hopefully make progress on the nuclear issue, make progress on the Lebanon ceasefire issue," he said.
A halt to fighting in Lebanon was one of the conditions for starting US-Iranian talks on Tehran's nuclear program and other issues. But Lebanese Civil Defence said that 20 people had been killed by Israeli strikes in Lebanon on Saturday, hours after a truce there took effect.
Israel said it was responding to attacks from Hezbollah, while the Iran-backed group said it would not allow Israel "freedom of movement" in Lebanon.
Israel said it is not party to the Iran-US deal, and would not withdraw from areas it had captured.
Lebanon's state news agency NNA said Israeli warplanes and drones had struck locations across southern Lebanon and the Bekaa Valley on Saturday, both Hezbollah strongholds.
An Israeli military official said Hezbollah fired more than 50 projectiles at Israeli forces in southern Lebanon overnight, and that Israel had attacked Hezbollah targets in response.
A military statement said Israel was committed to the ceasefire but would continue to act against any threat to Israel or its forces.
Lebanon's health ministry says 4057 people have been killed in Israeli attacks since March 2, including medics, women and children, though it does not specify how many of the dead were combatants.
Israeli authorities say at least 32 soldiers and four civilians have been killed in fighting with Hezbollah.
