The director of the Getty Museum in Los Angeles is to recommend returning priceless artefacts to Greece.
Michael Brand is director of the Getty Museum
The Greek government alleges items were originally removed from the country illegally, although it is not known when they were taken.
The museum may now return some of the four disputed antiquities, following a meeting with Greek Culture Minister Giorgos Voulgarakis.
The Getty is also in a dispute over items allegedly trafficked from Italy.
Former curator Marion True faces charges in Italy involving 35 artefacts bought between 1986 and the late 1990s. She has denied the claims but resigned from the museum.
Greece has been fighting a campaign for the return of artefacts from its history.
Part of its long-running campaign has been its call for the return of the Elgin Marbles, housed at the British Museum, which the UK government has so far refused.
Greece has called on the Getty Museum to hand back four artefacts including a 6th Century marble statue of a young woman and a gold wreath.
No details of which of the items may find their way back to Greece have been revealed.
Museum director Michael Brand met with Greek officials in Athens, where he agreed to suggest to his board of trustees that items be returned.
He said handing back the artefacts could lead to a "fruitful co-operation" between the countries which could include long-term loans of museum pieces.
"Talks are ongoing and representatives will be appointed to seek resolution of the matter within the next two or three months," said Mr Brand.