Several Iranian state media outlets cited an "informed source" as saying that Iran had turned around six "offending ships" on Monday morning that had attempted to cross the strait without its permission. One of the vessels, the source said, had had "an accident".
"As previously announced, the traffic route in the Strait of Hormuz is the route specified by Iran, and other routes are contaminated and have no way out," the Iranian state media reports quoted the source as saying.
Trump launched his renewed bombing campaign to punish Iran after Tehran fired on ships using a route through the strait that has been promoted by the United States, which has told vessels to sail close to the coast of Oman.
Iran says ships may pass only through a channel that runs closer to its own coast, which it controls and where it intends to impose transit fees.
The two weeks of renewed U.S. bombing killed scores of people in Iran and destroyed bridges and tunnels across the south as well as military targets. Four U.S. service members were killed by Iran's return fire against U.S. bases in neighbouring Arab states. Iran also struck civilian infrastructure in Gulf countries in what it said was retaliation for U.S. strikes on civilian targets.
Last week Iran's Houthi allies threatened to extend the disruption to global oil supplies to a second major waterway by announcing a blockade of Saudi Arabia's oil industry in the Red Sea, sending oil prices even higher.
The halt to the renewed U.S. bombing campaign leaves no clear indication of what leverage Washington can exert to achieve Trump's aim to break Iran's grip on the strait.
Washington and Tehran reached an agreement in June on a framework for talks meant to take place by the end of August to resolve major issues such as Iran's nuclear programme.
But the sides have disputed the meaning of the memorandum's language about the Strait of Hormuz, with Washington insisting it requires Tehran to allow free travel while Iran says it grants it the authority to supervise transit.
Iran aims to formalise its control over the strait in an agreement with Oman, which controls the opposite shore. A senior Omani delegation was in Tehran over the weekend discussing the strait and Iranian Foreign Ministry spokesperson Baghaei said those talks went well.