US Vice President JD Vance said on Saturday he expects to go to Switzerland soon for talks with Iran, even as Tehran's high command was reported as saying it would shut the Strait of Hormuz due to what it called US and Israeli truce violations, while the US military said it was monitoring the waterway to ensure that the Strait of Hormuz remains open.

Iran's top joint military command, ​Khatam al-Anbiya Central ‌Headquarters, said the waterway, vital to global oil shipments, would be closed to vessel traffic, citing alleged violations of a ceasefire agreement by the US and Israel, Iran's Mehr state news agency reported.

It said that the closure was the "first step" in response to what it described as breaches of commitments and warned that further measures would be taken if "aggression" continued.

The Mehr report emerged as Vance told Fox News in an interview that he was confident the ceasefire agreed in Washington's 14-point deal with Tehran would hold, and that he saw no evidence that Hormuz was closed.

The US military on Saturday denied Iran's claims that it had closed the Strait of Hormuz, saying the critical waterway remained open and that US forces were monitoring the situation to ensure that continued.

"Iran does not control the Strait of Hormuz," US Central Command spokesperson Navy Captain Tim Hawkins told Reuters. "Traffic continues to flow, and US forces are monitoring the situation to ensure this remains the case."

Iran's Islamic Revolutionary Guard Corps declared the Strait of Hormuz shut earlier on Saturday and warned ships not to approach the waterway, casting new doubt on the future of a ceasefire agreement between the US and Iran meant to pave the way for in-depth peace talks.