The J. Paul Getty Museum has agreed to return two artworks at the center of a major dispute with Greece, officials said Monday.

In a joint statement, Voulgarakis and Getty Director Michael Brand said negotiations would continue on the return of two other ancient masterpieces that Greece claims were illegally excavated and smuggled out of the country.

Voulgarakis said he was "extremely satisfied" with the decision and voiced optimism that similar moves would follow from the Getty and other international museums.

Getty spokesman Ron Hartwig said details were still being finalized about when the two pieces might return to Greece. The artifacts have been displayed at the Getty Villa in Malibu, Calif., which houses the museum‘s extensive antiquities collection.

The agreement came after intense pressure from Greek authorities, who said they were able to prove the works were looted.

Authorities have stepped up their campaign for the return of looted antiquities, thousands of which are believed to be displayed in museums and private collections worldwide.

One villa belonged to the Getty‘s former antiquities curator, Marion True, who is on trial in Rome for allegedly having knowingly purchased stolen artifacts for the museum from Italy. True, who was out of Greece during the raids, has denied any wrongdoing.

Last month, the Getty said a tentative agreement had been reached in negotiations with Italian authorities over allegedly illegally obtained antiquities. Italy has been negotiating for the return of dozens of artifacts.