The Iranian delegation was led by chief negotiator Mohammad Baqer Qalibaf and included Foreign Minister Abbas Araqchi as well as senior security, central bank and oil officials, Iranian media said.
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.
This 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.
The IRGC warned ships would be at risk if they approached the waterway, a vital conduit for global oil and gas supplies. Iran cited what it called Israeli "crimes" in Lebanon and a US violation of commitments to establish a ceasefire.
US Central Command said 55 merchant ships had transited the strait on Saturday, moving large amounts of cargo and more than 17 million barrels of oil to global markets, and that US forces would ensure the flow of ships continued.
US President Donald Trump in a social media post on Saturday wrote that no toll will be charged for passage through the Strait during or after the 60-day ceasefire - unless the US imposes 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 is not completed.
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.
He said that, as long as the agreement was only on paper, the flow of Middle East energy would remain halted.
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 agreed in Washington's 14-point deal with Tehran would hold, and that he had seen no evidence that the strait was closed.
The US vice president left for Switzerland shortly after 4pm on Saturday.
Negotiators would likely have a "couple days of talks," Vance told reporters before boarding a plane at Joint Base Andrews in Maryland.
"I can only be there for a day or two," Vance said.
"I think we're going to hopefully make progress on the nuclear issue, make progress on the Lebanon ceasefire issue."
One of the conditions for starting 60 days of US-Iranian talks on Tehran's nuclear program and other issues is a halt to fighting in Lebanon.
However, 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 Defense Forces said on X it was responding to attacks from Hezbollah, while the Iran-backed group said it would not allow Israel "freedom of movement" in Lebanon.
Israel is not party to the Iran-US deal, and will keep its forces in the Lebanese territory it occupies.
A US official had said the truce took effect at 4pm on Friday.
The Israeli broadcaster Channel 12 reported that the prime minister and defence minister had instructed the military to hold fire in Lebanon, but that it 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 what it described as Hezbollah targets in response.
A military statement said Israel was committed to the ceasefire and would continue to act against any threat to Israel or its forces.
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