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Trump told reporters that negotiations had progressed well and suggested an agreement could be reached within days, while earlier stating that the strategic waterway would reopen soon, either through diplomacy or stronger US action.
The Strait of Hormuz, a vital route for global oil and gas shipments, has remained at the centre of regional tensions and of ongoing diplomatic efforts.
US Treasury Secretary Scott Bessent said there was a possibility of reaching an agreement by Wednesday or Thursday, while Secretary of State Marco Rubio confirmed that Washington is participating in discussions between Oman and Iran to facilitate maritime traffic through the strait.
Despite Trump's comments, Iran's Foreign Ministry has maintained that there are no direct negotiations with the United States, saying its talks are being held with Oman on the management of shipping through the Strait of Hormuz.
According to reports, the United States, Iran and Oman are nearing an interim arrangement to restore safe passage through the strait for an initial 60-day period, although no agreement has yet been formally announced.
The diplomatic efforts come amid ongoing security concerns after a merchant vessel was struck by an unidentified projectile in the Strait of Hormuz, while a separate commercial ship sank in the Red Sea after another attack.