The Adrian Darya, formerly called Grace 1, was now headed for the southeastern Turkish port of Iskenderun, tracking site Marine Traffic showed.
It is the third time the ship has changed destination in 10 days. Iskenderun is roughly 200 km north of the Baniyas refinery in Syria - the suspected original destination of the tanker.
Carrying 2 million barrels of oil, the Adrian Darya was released from detention off Gibraltar in mid-August after a five-week standoff over whether it was carrying Iranian oil to Syria in violation of European Union sanctions.
The U.S., which says the tanker is controlled by the Iranian Revolutionary Guards it considers a terrorist group, has warned countries in the region not to assist the vessel.
An Iranian government spokesman was quoted on Monday as saying Iran had sold the oil aboard the tanker and that the vessel’s owner, whose identity he did not disclose, would decide its destination.
After its release, it stated that its destination was the Greek port of Kalamata, then Turkey’s Mersin. On Thursday, it abruptly changed course, making almost a U-turn away from the Turkish coast.
While west of Cyprus on Friday morning, it did a similar maneuver, doubling back on itself.