In response, Iranian forces seized two Greek tankers in the Arabian Gulf last month after Iran said it would take "punitive action" against Greece.
Iran also appealed against the original court decision, a legal source told Reuters. The result of the appeal has not yet been officially revealed.
"The action for the reversal of the ruling was accepted by the court," the source said. "It will be hard to overrule that [the appeal court's ruling]."
It is not known whether the US or Greek governments will challenge the ruling, which was made in the appeals court of the region of Chalkis.
Greece had called Iran's seizure of the two Greek tankers in the Gulf "piracy".
Russian crew on board impounded vessel
The case arose when Greek authorities in April impounded the Iranian-flagged Lana, formerly the Pegas, with 19 Russian crew members on board, near the coast of the southern island of Evia because of EU sanctions.
The ship was soon released because of complications regarding its ownership. The US in May confiscated part of the Iranian oil cargo and transferred it to another ship, following the initial Greek court ruling.
Mr Kozanidis declined to disclose the name of the company he represents but told Reuters the case wrelated to unpaid towing services.ing company, represented by lawyer George Kozanidis.w
Mr Kozanidis declined to disclose the name of the company he represents but told Reuters the case was related to unpaid towing services.