The Iranian tanker caught in a standoff between Tehran and the West was sailing to Greece on Monday (August 19).
The Grace 1, renamed the Adrian Darya 1, left Gibraltar around 2100 GMT on Sunday (August 18), according to shipping data.
It showed that the vessel was heading to Kalamata in Greece.
Just hours before its departure, the British territory rejected a U.S. request to detain the tanker further.
British Royal Marines seized the Grace 1 near Gibraltar in July on suspicion of carrying oil to Syria, a close ally of Iran, in violation of European Union sanctions - something Iran denied.
That led to heightened tensions on international oil shipping routes through the Gulf.
Two weeks later, Iran's Revolutionary Guards seized the British-flagged Stena Impero in the Strait of Hormuz waterway for alleged marine violations.
The Grace 1's detention ended last week.
But a federal court in Washington on Friday (August 16) issued a warrant for its seizure, that of the oil it carries and nearly $1 million on the grounds that it had links to Iran's Islamic Revolutionary Guard Corps, which it says is a terrorist organization.
Gibraltar said on Sunday it couldn't comply because it was bound by EU law.
A senior Iranian lawmaker was quoted as saying that the crisis in Iran's ties with Britain wouldn't be over until the tanker reached its destination.
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