Shipping data showed the Grace 1, renamed the Adrian Darya 1, leaving Gibraltar around 11pm on Sunday, and is believed to be heading to Kalamata in Greece.
Authorities in Gibraltar released the tanker last week but on Friday a federal court in Washington issued a warrant for its seizure, along with its cargo of 2.1 million barrels of light crude oil, and nearly $1m (£824,000).
However, on Sunday Gibraltar said it could not comply with that request because it was bound by EU law.
Washington had attempted to detain the ship on the grounds it had links to Iran’s Islamic Revolutionary Guards Corps (IRGC), which it has designated a terrorist organisation.
The release comes amid a growing row between Iran and the west after Donald Trump pulled Washington out of Tehran’s nuclear deal with world powers more than a year ago.
Shortly after the tanker was detained in early July near Gibraltar, a British overseas territory, Iran seized the British-flagged oil tanker Stena Impero in the Strait of Hormuz, which remains in the Islamic Republic.
Iran has warned the US against any new attempt to seize its tanker in open seas after it left Gibraltar.
Asked whether the US could renew its seizure request, Abbas Mousavi, a spokesperson for the Iranian Ministry of Foreign Affairs, said: “Such an action ... would endanger shipping safety in open seas. We have issued a warning through official channels, especially the Swiss embassy.”
Switzerland represents American interests in Iran, which has no diplomatic relations with the US.
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After the US unsealed a warrant on Friday to seize the vessel and its cargo, US officials told reporters the oil abroad the ship was worth some $130m (£107m) and it was destined for a designated terrorist organisation.
The unsealed court documents argued Iran’s IRGC is the ship’s true owners through a network of front companies.
But authorities in Gibraltar said that, unlike in the US, the IRGC is not a designated terrorist organisation under EU, British or Gibraltan law.
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Iran has not disclosed the Adrian Darya 1’s intended destination and has denied it was ever headed for Syria.
The chief minister of Gibraltar, Fabian Picardo, said he had been assured in writing by the Iranian government the tanker would not unload its cargo in Syria.
The Astralship shipping agency in Gibraltar, which has been hired to handle paperwork and arrange logistics for the Adrian Darya 1, told reporters a new crew of Indian and Ukrainian nationals had been expected to replace the sailors on board.
Additional reporting by agencies