ATHENS- Greece said on Tuesday it had not had a request for an oil tanker at the centre of a row between Iran and the U.S. to dock at one of its ports, as Washington warned Greece against helping the vessel.

The Adrian Darya 1 -- formerly the Grace 1 -- left Gibraltar on Aug 18. Ship-tracking data on Tuesday showed the vessel was heading towards the Greek port of Kalamata on the southern coast of the Peloponnese and was scheduled to arrive on Aug. 26.

"The vessel is cruising at low speed and there is still no formal announcement that it will arrive at Kalamata. The Merchant Marine Ministry is monitoring the matter along with Greece's Foreign Ministry," a shipping ministry spokesman said.

The ship was released from detention off Gibraltar after a five-week standoff over whether it was carrying Iranian oil to Syria in violation of European Union sanctions.

Soon after the detention order was lifted, a U.S. federal court ordered the seizure of the vessel on different grounds, but that petition was rejected by Gibraltar.

Tehran said any U.S. move to seize the vessel again would have "heavy consequences".

Earlier, the United States said it had conveyed its "strong position" to the Greek government over the tanker, which is carrying about 2 million barrels of oil.

The issue will be a major foreign policy test for Greek Prime Minister Kyriakos Mitsotakis, a pro-western conservative elected in July.

Any efforts to assist the tanker could be construed as providing material support to a U.S.-designated foreign terrorist organization, which has immigration and potential criminal consequences, a U.S. State Department official said.

A Greek diplomatic source cited by the state Athens News Agency said the country was in communication with the United States on the matter, but did not say what Greece would do.

"(The U.S.) position on the specific issue is known and has been communicated not only to Greece but other states and ports in the Mediterranean."

It is standard practice for a vessel to give notice 48 hours before docking at a port, Greek officials said.

It was unclear where the ship might head if Greece refused it permission to dock. Cyprus, further east, has bitter experience from seizing Iranian products destined for Syria; munitions it confiscated exploded in 2011, causing the island's worst peace-time disaster.

Washington wants the tanker detained on the grounds that it had links to Iran's Islamic Revolutionary Guard Corps, which it has designated a terrorist organisation.

European Union nations ban oil sales to Syria and the United States has sanctions on Iranian oil sales.

(Reporting by Michele Kambas and George Georgiopoulos; editing by John Stonestreet) ((michele.kambas@thomsonreuters.com;))