The ship, with its cargo of 2.1 million barrels of oil, and crew of 29 from India, Russia, Latvia and the Philippines, was seized with the help of British marines on July 4, after the government of Gibraltar, a UK territory, suggested it was heading for Syria in breach of European Union (EU) sanctions, the BBC reported.
Previously known as Grace 1, the Adrian Darya-1 was released on August 18 after Iran gave assurances that it would not discharge its cargo in Syria.
In a statement on Friday night, the US Treasury said the Adrian Darya 1 was being used to transport 2.1 million barrels of Iranian crude oil for the benefit of Iran's Islamic Revolutionary Guard Corps (IRGC) - a branch of the country's armed forces that the US has designated a terrorist organisation.
It insisted that ships like Adrian Darya 1 were being used to sell oil illicitly to fund Iran's "malign activities and propagate terrorism".
US Secretary of State Mike Pompeo added in a tweet that Washington had "reliable information" the vessel was on course to Tartus, a major Syrian port city which is also home to a Russian naval base.
He added that it was "a big mistake" to trust any assurances about the ship from Iranian Foreign Minister Javad Zarif.
In earlier talks, Iran said that oil aboard the ship had already been sold, but it did not revealed the identity of the buyer, reports the BBC.
After the Adrian Darya-1 left Gibraltar, it listed the Greek port Kalamata as its final destination.
According to publicly available tracking data, the tanker had changed its final destination to Iskenderun in eastern Turkey, about 40 km from the Syrian border.
But Turkish Foreign Minister Mevlut Cavusoglu said on Friday that the tanker had changed course several times and insisted that it was heading for Lebanese waters instead.
( With inputs from IANS )