The Iranian tanker caught in a standoff between Tehran and the West left Gibraltar on Sunday night, shipping data showed, hours after the British territory rejected a US request to detain the vessel further.
British Royal Marines seized the tanker in Gibraltar in July on suspicion it was carrying oil to Syria, a close ally of Iran, in violation of European Union sanctions.
That triggered a series of events that have heightened tensions on international oil shipping routes through the Gulf, including the seizure of the British-flagged oil tanker Stena Impero, which remains held by the Islamic Republic.
Analysts had said the Iranian ship's release by Gibraltar could see the Stena Impero go free.
The Grace 1, renamed the Adrian Darya 1, left anchorage off Gibraltar around 11pm, Refinitiv shipping data showed. Its destination was not immediately clear.
Iran's ambassador to Britain, Hamid Baeidinejad, had written on Twitter earlier that the vessel was expected to leave on Sunday night, adding that two engineering teams had been flown to Gibraltar.
The tanker's detention ended last week, but a federal court in Washington on Friday issued a warrant for the seizure of the tanker, the oil it carries and nearly $1 million.
Gibraltar said on Sunday it could not comply with that request because it was bound by EU law.
"The EU sanctions regime against Iran – which is applicable in Gibraltar - is much narrower than that applicable in the US," the government said in a statement.
"The Gibraltar Central Authority is unable to seek an Order of the Supreme Court of Gibraltar to provide the restraining assistance required by the United States of America."
Washington had attempted to detain the Grace 1 on the grounds that it had links to Iran's Islamic Revolutionary Guard Corps (IRGC), which it has designated a terrorist organisation.
US President Donald Trump said on Sunday that "Iran would like to talk," attributing the willingness to economic conditions in the country, when asked on Sunday by reporters about the status of the tanker.
“Iran would like to talk but they just don’t know how to get there. They are very proud people. But their economy is crashing, crashing.
“Inflation is through the roof. Their economy is doing really badly, they are not selling oil. We put the sanctions on, the oil is selling much less, much less than we thought. It’s like a trickle.
“They very much want to make a deal, they just don’t know how to make a call, because they are proud people and I understand that.
“But I have a feeling that things with Iran could work out, or maybe not."
Iran has denied the tanker was ever headed to Syria.
Tehran said it was ready to dispatch its naval fleet to escort the tanker if required.
"The era of hit and run is over ... if top authorities ask the navy, we are ready to escort out tanker Adrian," Iran's navy commander, Rear Admiral Hossein Khanzadi, was quoted as saying by Mehr news agency.
Earlier on Sunday, video and photographs showed the tanker flying the red, green and white flag of Iran and bearing its new name, painted in white, on the hull. Its previous name, 'Grace 1', had been painted over.
The initial impounding of the Grace 1 sparked a diplomatic row that escalated when Tehran seize a British-flagged oil tanker in the Gulf two weeks later. That tanker, the Stena Impero, is still detained.
The two vessels have since become pawns in a bigger game, feeding into wider hostilities since the United States last year pulled out of an international agreement to curb Iran's nuclear programme, and reimposed economic sanctions.
Iran has denounced US efforts to set up an international maritime security coalition in the Gulf and insisted regional countries could protect the strategic waterway and work towards signing a non-aggression pact.
On a trip to Kuwait on Sunday, Iranian Foreign Minister Mohammad Javad Zarif said in a tweet that "Iran's proposal for Regional Dialogue Forum and non-aggression pact trumps reliance on extraneous actors".
The Grace 1 had originally flown the Panamanian flag but Panama's Maritime Authority said in July that the vessel had been de-listed after an alert that indicated the ship had participated in or was linked to terrorism financing.