Iran's ambassador to Britain, Hamid Baeidinejad, had earlier announced on Twitter that the ship was expected to leave Sunday night.
"The Gibraltar Central Authority is unable seek an Order of the Supreme Court of Gibraltar to provide the restraining assistance required by the United States of America", a Gibraltar government statement said on Sunday.
On Sunday, a video published by the Reuters news agency showed the ship displaying a new name, having changed it from Grace 1 to Adrian Darya-1.
The Grace 1's detention ended last week, but on Friday a federal court in Washington issued a warrant for the seizure of the tanker, the oil it carries and almost $1 million.
Among the charges laid out in the US warrant is that the tanker was facilitating terrorism because of the involvement in Iran's oil industry of the Islamic Revolutionary Guard Corps, which is designated a terrorist organization by the United States.
A Gibraltar judge had ordered the Grace 1 tanker released on Thursday, weeks after authorities seized the vessel on suspicion of transporting oil to Syria in breach of European sanctions. They should now be able to sail on to a destination agreed with Iran and the owner of the tanker - the National Iranian Oil Company.
The Government says however, that it is unable to seek a Supreme Court Order to provide the restraining assistance requested because of the operation of European Union law, and differences in sanctions regimes applicable to Iran in the European Union and the US.
Grace 1, which had been detained in the semi-autonomous British Overseas Territory of Gibraltar on the Spanish coast last month, has been renamed the Adrain Darya based on the Persian word for sea.
However the vessel's anchor still remains down.
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 U.S. past year pulled out of an global agreement to curb Iran's nuclear programme, and reimposed economic sanctions.
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". Analysts had said the Iranian ship's release by Gibraltar could see the Stena Impero go free.