The president had earlier posted an image of a map showing the Strait as a new US territory, appearing to restate his threat to claim sovereignty over the passage from last week.
US President Donald Trump on Tuesday said there were "no talks or conversations" taking place or planned with Tehran while also claiming that the Strait of Hormuz was "open and operating."
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In a post on Truth Social, Trump said that "all water mines have been removed or detonated" in the strategic waterway and that the US' naval blockade remained "in full force and effect."
The president had earlier posted an image of a map showing the Strait - a vital energy transit chokepoint - as a new US territory, appearing to restate his threat to claim sovereignty over the passage from last week.
It comes as Iran's top negotiator said the Strait of Hormuz would not open until the US lifted its blockade and released frozen Iranian assets.
Parliament speaker Mohammad Bagher Ghalibaf said on Tuesday that the crucial waterway would remain shut to cargo traffic until Washington meets Tehran's demands.
"I want to state clearly that the Strait of Hormuz will not be opened until the American commitments stipulated in the memorandum of understanding... are implemented," Ghalibaf said in a speech broadcast on state-run TV.
He listed the end to the blockade, the lifting of oil sanctions and unfreezing of Iran's assets abroad among Tehran's demands.
Meanwhile, an unidentified projectile damaged the engine room of a ship and “resulted in a crew casualty” early Tuesday morning, as the vessel was trying to transit the Strait of Hormuz off the coast of Oman, the UKMTO said, citing a report from the company's security office.
The maritime monitoring agency did not release any details about the ship or its cargo, and it was not clear whether the crew member was killed in the attack or wounded.
It said the Omani Coast Guard was assisting other crew members and that authorities were investigating.
There has been growing concern about oil spilling into the Persian Gulf and other area waters from vessels damaged as they have attempted to transit the Strait, but the UKMTO said no environmental damage had been reported in the latest attack.
Tehran's forces effectively closed the Strait — through which roughly one-fifth of the world’s traded oil supplies passed before the war — after Israel and the US attacked Iran on 28 February.
The US is also currently blockading all Iranian shipping traffic through the Strait.
With negotiations between the two sides stalled, Tehran has been holding separate talks with Oman on a plan to manage ships transiting the Strait and said Monday it was finalising details for a joint statement.
Trump reacted angrily, reportedly telling Fox News in a telephone interview that the US would bomb "the s*** out of" Oman if it “gets in the way”.
Trump also provoked a fiery response from Tehran after he said last Friday that he would soon be declaring the Strait "a territory of the United States".
Responding to the comments in a post on X, Iran's Deputy Foreign Minister Kazem Gharibabadi said that "the Strait of Hormuz has been Iranian, is Iranian, and will remain Iranian."
"This Strait will only be closed and opened under Iran's command, and as long as you do not accept the reality of defeat and cease your fanciful delusions, Iran will continue to enforce the blockade," Gharibabadi added.
The Strait of Hormuz is roughly 35 kilometres wide at its narrowest, meaning both Iran and Oman operate the waterway.
Muscat has maintained diplomatic relations with both Iran and the US throughout the war as a neutral mediator.