The J. Paul Getty Museum inched a step closer to relinquishing ownership of one of its most prized artifacts, a 2,400-year-old statue of a goddess claimed by Italy, at a conference of international experts to discuss the artifact this week, its director said.

The Getty has not reached a formal conclusion based on the conference, which was convened at the museum on Wednesday and was closed to the public. But museum officials and some of the experts who attended said their discussions buttressed what the museum says are its own suspicions that the statue, acquired by the Getty in 1988, might have been illegally excavated in southern Italy.

“There was no dramatic single conclusion, no eureka moment, but it is certainly helping us narrow down the focus,” Michael Brand, the museum’s director, said in an interview. “It would be fair to say that most of the discussion focused on Sicily.”

The statue’s precise provenance, like that of many antiquities, is unknown. But the Italian government asserts that it was looted in recent decades, and Mr. Brand said the Getty’s own investigation into its acquisition had revealed “problems.”

The museum offered to relinquish title to the statue in November, when negotiations with Italy over the statue and 51 other artifacts broke down. It said it would study the disputed object for a year before making a final decision. At the time, the museum also unilaterally decided to return 26 of the objects.

If the Getty turned up persuasive evidence that the statue came from a different archaeological source country, like Libya, or that it had been found and removed from Italy before 1939, when a ban was imposed on such exports, that could furnish a justification for keeping it. But so far no such clear evidence has emerged, Mr. Brand said.

He said: “We intend to resolve this whole matter within the next six months, and we will. At some point our board of trustees has to agree to take it out of the public trust and possibly give it to someone else. We should do that very carefully.”

The dispute has been part of a painful process of self-examination at an institution rocked by other scandals and disputes in the last decade. The Getty’s former antiquities curator, Marion True, remains on trial in Italy on charges of conspiring to acquire looted objects for the museum. An investigator testified at the trial last year that the goddess had been exported after an illegal excavation in Morgantina in central Sicily, at one time a richly developed part of the Greek empire.

Malcolm Bell III, an archaeologist at the University of Virginia who attended Wednesday’s conference, said that there was so far no conclusive evidence that the statue came from Morgantina, where he conducts research, but added, “I think there’s a very strong probability that it came from Sicily.”

“Until we know the find spot, we can’t say with certainty,” he said.

A spokeswoman for the Italian Culture Ministry in Rome declined to comment on the meeting. The Getty said that Italy had not responded to two invitations to take part.

The statue, a rare example of a cult figure considered the embodiment of a deity and used in Greek temple rituals, is viewed as the most historically significant artifact that Italy is demanding that the Getty return. The museum bought the piece for $18 million, a record for an ancient artifact at the time of its purchase.

Italy, Greece and many archaeologists argue that museums like the Getty motivate looters to ransack ancient sites and middlemen to trade in illicit antiquities because of their willingness to pay huge prices to build their collections.

Experts in art conservation and in soil, pollen and stone analysis convened at the recently refurbished Getty antiquities museum, a Greek-inspired villa in nearby Pacific Palisades. They spent about an hour at the villa inspecting the statue, a seven-and-a-half-foot standing figure with windswept robes carved in limestone, a placid expression on her smooth marble face.

Rosario Alaimo, a professor of geochemistry at the University of Palermo, presented research suggesting that the limestone appeared to have been quarried in eastern Sicily, the Getty said. The museum said that John Twilley, a New York conservator and soil expert, presented a chemical analysis of the dirt removed from holes in the statue at the time of its acquisition, while stating that further study would be required before conclusions could be drawn.

A new study of pollen remains by Pamela I. Chester, an archaeological palynologist from New Zealand, said the dirt seemed to come from an open landscape that had been extensively cultivated, rather than from virgin forest.

Although the Getty has said that there is no evidence for the Italians’ claim that the statue was dug up at Morgantina, it bought the piece without clearly establishing its background. Ms. True, the former curator, purchased the statue through Robin Symes, a London-based art dealer who told the museum that it came from the collection of a Swiss supermarket magnate.

“Without any doubt, that was invented by the dealer,” Mr. Bell said. “It was a much more dubious context. A person convicted by the Italians, Canavesi, seems clearly to have had it.” Renzo Canavesi, owner of a tobacco shop in Switzerland, had initially claimed that his family owned the statue from 1939 until 1986, when he said he sold it to Mr. Symes.

In a 1997 museum catalog the statue was described as “the most important discovery of a Greek statue in the past decade” and “the only complete example of the most important type of sculpted figure to survive from antiquity.”

The fate of 21 other objects remains unresolved. For the moment there are no negotiations with the Italian government, Mr. Brand said. He also said the museum had no intention of returning a prized bronze sculpture taken from the sea in international waters to which he said Italy had no legal claim.

“From our point of view, there’s nothing more we can do about the bronze,” he said.