The British-flagged Stena Impero tanker left Iran's Bandar Abbas port on Friday and was heading for Dubai so the crew could be repatriated, the owner said, after the ship was detained in July by Iranian forces during a row with Britain.
The Stena Impero was seized by Iran's Revolutionary Guards in the Strait of Hormuz waterway for alleged marine violations two weeks after Britain detained an Iranian tanker off the territory of Gibraltar. The Iranian ship was released in August.
"The ship is on the move," Erik Hanell, the chief executive of Sweden's Stena Bulk, the ship's owner, told Reuters.
He said the company had a well-prepared security plan for the vessel once it left Iranian waters, adding that it was expected to reach international waters at about 1000 GMT.
The seizure of the ship on July 19 ratcheted up tension in the region after attacks in May and June on other merchant vessels in Gulf waters, which the United States blamed on Iran, a charge Tehran denied.
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Stena Bulk said the Stena Impero was heading to Dubai in the United Arab Emirates, on the opposite side of the Gulf, where the crew would receive medical checks and a debriefing.
Iran released seven of the ship's 23 crew earlier this month.
"The families of crew members have been informed and the company is currently making arrangements for the repatriation of its valued seafarers at the earliest possible opportunity," the company said in a statement.
Refinitiv tracking data showed the vessel was heading for Dubai's Port Rashid, about 250 km (155 miles) from Bandar Abbas. At normal tanker speed, it would arrive within half a day.
The Ports and Maritime Organization of Iran in Hormozgan Province said in a statement the ship had moved from Bandar Abbas at 9 A.M. Iran time (0530 GMT).
It said the judicial file on the vessel remained open and the process of looking into "violations" by the ship was ongoing.
Iran's Foreign Ministry had said on Wednesday that the detention order had been lifted but the investigation continued.
Stena Bulk said on Wednesday it was not in negotiations with Iran and said it was not aware of any formal charges against the crew or the company.
Relations between the United States and Iran have become more strained since Washington withdrew last year from a global pact to rein in Tehran's nuclear programme and imposed sanctions on the country aimed at shutting down Iranian oil exports.