The gravestone (left) depicts a warrior with spear, shield and sword
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The J Paul Getty Museum in Los Angeles has agreed to return a pair of disputed ancient sculptures to Greece following renewed calls for their restitution.
The artefacts in question are a 6th Century BC relief from the island of Thassos and a 4th Century BC tombstone from the ancient city of Thebes.
Negotiations continue over the return of two more antiques, said Greek culture minister Giorgos Voulgarakis.
Greece has offered a long-term loan of antiquities to the Getty in return.
In a statement, the museum said it had reached its decision after "a thorough internal investigation... which concluded it would be right to return the works".
The contested items, which include a marble torso and a gold funerary wreath, were bought by the museum for $5.2m (£2.8m) in 1993.
The Getty is currently involved in another dispute over items allegedly trafficked from Italy.