A memorandum of understanding on a path to end the war, agreed a week ago, calls for the Strait to be reopened and a halt to all hostilities, including in Lebanon, which Washington's ally Israel invaded in March.
But with little sign of an end to fighting there, Iran said on Saturday it had shut the Strait again.
US officials have disputed the Strait is closed and said 55 merchant ships had crossed it on Saturday. But on Sunday Iran's Fars news agency cited a military source as saying no new permits were being issued for ships to cross until further notice.
As often the case with major developments potentially affecting the global economy during the war, the announcement the strait was again shut took place on the weekend with markets closed, making it difficult to assess the impact.
US President Donald Trump said he agreed on last week's memorandum of understanding to avert a global depression from high oil prices caused by shutting the strait.
Since the agreement was announced, oil prices have tumbled to levels unseen since the war started, but a return of Iran's effective blockade could see them surge again when markets reopen on Monday.
Iran's foreign ministry spokesperson, Esmail Baghaei, said Sunday's talks in the scenic Qatari-owned Swiss mountain resort of Buergenstock, involving mediators Qatar and Pakistan as well as Iran and the United States, would last for just one day.
Since Washington had failed to guarantee a ceasefire in Lebanon, the talks would cover only the implementation of the memorandum itself and not the substantive issues foreseen for the next stage of negotiations, Beghaei said.
The memorandum of understanding foresees 60 days of talks on issues such as curbing Iran's nuclear program in return for the lifting of international sanctions. Iran is already expected to receive initial economic benefits, such as sanctions waivers and the unfreezing of blocked assets.
Vance leads the US delegation, opposite Iran's parliament speaker, Mohammed Baqer Qalibaf. They previously met at the only known face-to-face talks so far, more than two months ago.
"I think we're going to hopefully make progress on the nuclear issue, make progress on the Lebanon ceasefire issue," with a "couple days of talks" likely, Vance told reporters at Joint Base Andrews in Maryland before departing.
On Saturday, Iran's Revolutionary Guards, accusing Israel of "crimes" in Lebanon that violated US commitments to the ceasefire, said ships would be at risk if they approached the Strait, which carried a fifth of global oil supplies before the US and Israel launched attacks on February 28.
Ceasefires have been repeatedly announced in Lebanon, most recently on Friday, but appear to have had little impact so far on the fighting there, with more than a million people driven from their homes by Israel's invasion.
Trump's memorandum to end the war, which he jointly launched alongside Israeli Prime Minister Benjamin Netanyahu in February, is deeply unpopular in Israel, which did not participate in the peace talks.
Netanyahu's government says it will not withdraw from a swathe of Lebanon it seized after Hezbollah fighters fired across the border into Israel in solidarity with Tehran.
The Iranian delegation at the talks includes Foreign Minister Abbas Araqchi as well as senior security, central bank and oil officials, Iranian media said. In addition to Vance, the US negotiating team includes envoys Steve Witkoff and Jared Kushner, Trump's son-in-law.
In an interview with Fox News before leaving the United States, Vance said he was confident the ceasefire would hold and he had seen no evidence of the Strait of Hormuz being closed.
After Trump and Netanyahu launched the war in February, they said their aims were to destroy Iran's nuclear program, halt its ability to threaten neighbours with missiles and proxy forces, and make it possible for Iranians to topple the government.
None of those objectives has been achieved, although US officials say they inflicted severe damage on Iran's military and still expect a strong agreement that will prevent Iran from obtaining a nuclear weapon.
A poll by Israel's Hebrew University, provided to Reuters, showed about 92 per cent of Israelis believe Iran benefited more than Israel from the joint Israeli-US military campaign, while just 8 per cent see Israel as having emerged victorious.
Almost 90 per cent of Israelis said war goals had not been met and fewer than 30 per cent believe Netanyahu's claims of major achievements.
