The US Justice Department alleged the ship was part of a scheme "to unlawfully access the US financial system to support illicit shipments to Syria from Iran by the Islamic Revolutionary Guard Corps," which Washington has designated a foreign terrorist organisation.
There was no comment from Britain or Gibraltar, its overseas territory.
Any detention order would ultimately have to come from Gibraltar's Supreme Court. So far, that has not happened and the ship is still free to sail.
Iran tanker prepares to leave after Gibraltar decides to free it: TV
Richard de la Rosa, managing director of Astralship, the vessel's shipping agent, told AFP the ship was preparing for departure.
"Within the next two days, she'll be going," he said.
"They're performing crew changes. She needs some reprovisioning," he said, adding new Indian and Ukrainian crew members were due to arrive on Sunday.
Gibraltar seized the ship on July 4 on suspicion it was transporting oil to Syria in breach of European Union sanctions, triggering a sharp deterioration in relations between Tehran and London. Iran has repeatedly denied this.
Iran subsequently detained the British-flagged tanker Stena Impero in what was seen as a tit-for-tat move.
On Thursday, Gibraltar's Supreme Court ordered the tanker released after the British overseas territory said it had received assurances from Iran that the Grace 1 would not head to any country subject to EU sanctions.
But in a last-minute twist on Friday, the United States, which is at loggerheads with Iran, issued the warrant.
It says the vessel and all the oil aboard are subject to forfeiture based on violations of US sanctions.
Tanker seizures: what we know
It also cites violations of bank fraud, money laundering and terrorism statutes.
The US State Department has also threatened to issue a visa ban on anyone working on the ship.
The US move comes after it tried -- and failed -- to block the tanker's release on Thursday.
The July 4 seizure came amid surging tensions in the Gulf after several alleged Iranian attacks on smaller tankers.
The US -- citing Tehran's threat to American allies -- expanded its military presence in the region with a new aircraft carrier task force, missile batteries and strategic bombers.
Iran called the detention of the Grace 1 an "illegal interception" staged by the United States, while Washington cheered it as "excellent news."
Ties between Tehran and Washington are at a low point since US President Donald Trump withdrew last year from a landmark 2015 nuclear deal between major powers and Iran, reimposing crippling unilateral sanctions.
On Friday, Iranian officials said the tanker was preparing to set sail under an Iranian flag and would be renamed the Adrian Darya for the voyage.
Tehran also denied it had made any promises about the ship's destination to secure the release.
"Iran has given no assurances over the Grace 1 not going to Syria to secure its release," a state media website quoted foreign ministry spokesman Abbas Mousavi as saying.
"The tanker's destination was not Syria... and even if it was, it did not concern anyone else."
But Gibraltar insisted it was.
Chief Minister Fabian Picardo said Gibraltar had deprived the Syrian regime of Bashar al-Assad of around $140 million worth of crude oil, according to a government statement.
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