The J. Paul Getty Museum has signed over to Greece ownership of two ancient artifacts at the heart of a major cultural heritage dispute, officials said Tuesday.

The private museum in Los Angeles agreed in July to return the two sculptures following intense pressure from Greece, which says they were illegally spirited out of the country.

The ownership deeds were signed in Los Angeles on Sunday in the presence of Greek officials, the museum and the Greek culture ministry said in a joint statement.

The artifacts — a sixth-century B.C. votive relief and a fourth-century B.C. carved tombstone — will be flown to Greece by the end of August, a ministry official said.

Talks will continue in Athens, the statement said, on the possible restitution of another two ancient treasures in the Getty collection — a gold wreath dating from about 400 B.C. and a sixth-century B.C. marble statue of a young woman.

"The two parties ... will explore the possibility of cooperation on matters of mutual interest," the statement said.

Museum and Greek officials have indicated that Greece would be prepared to offer the U.S. museum long-term loans of Greek antiquities.

The two artifacts to be flown back have been displayed at the Getty Villa in Malibu, Calif., which houses the museum's extensive antiquities collection. The Getty agreed to hand them over "after a thorough internal investigation, which concluded that it would be right to return the works," the statement said.

The marble relief, which depicts two women offering gifts to a seated goddess, was found by French archaeologists on the island of Thassos about 100 years ago and stolen from a storeroom. The Getty bought it in 1955.

The black stone tombstone, incised with the figure of a young warrior named Athanias, was acquired by the Getty in the early 1990s. Greek authorities say it was illegally excavated near Thebes — an antiquities-rich town some 56 miles northwest of Athens — between 1992-96.

Greek police have launched a crackdown on antiquities smuggling, with raids this year on two island villas whose owners are linked with the international art trade.