The battle between the world's richest museum and the Italian state took a turn for the worse yesterday when the Getty museum in California walked out of talks over the restitution of looted antiquities.

Michael Brand, the director of the Getty, has sent a closely argued, six-page letter to Francesco Rutelli, the Minister of Culture, saying he is "deeply saddened" by the failure to reach agreement after more than a year of talks, and announcing the end of "these present negotiations". Mr Rutelli's office said the letter had been received "with surprise and disappointment".

At the centre of the dispute is an enormous marble and limestone statue of the goddess Aphrodite, sold to the Getty for $18m (£10m) by a British antiquities dealer who was jailed last year. The statue, one of the glories of the Malibu museum, is claimed by the Italians to have been dug up by grave robbers in Morgantina, Sicily, and illegally exported to Switzerland, where the British dealer Robin Symes sold it on to the Americans.

The Americans point out that the man who sold the statue to Mr Symes, a Sicilian named Renzo Canavesi, provided a document stating that the statue had been privately owned since 1939, and that at least one authority on the archaeology of Morgantina says there is no evidence that Aphrodite came from there.

John Paul Getty, the oil billionaire who once said "the meek shall inherit the earth but not its mineral rights", took a swashbuckling approach to the task of filling his museum with masterpieces, and encouraged his employees to do the same. This helped it to become within a couple of decades the rival of far grander museums. But today, as nations such as Greece and Italy begin robustly to defend their rights to their own patrimony, the ruthlessness of old has become a liability.

In summer last year, the then curator of antiquities at the Getty museum, Marion True, was put on trial in Rome accused of acquiring antiquities illegally, a prosecution that sent a shock through the antiquities departments of some of the world's greatest museums. The Metropolitan Museum in New York and the Boston Museum of Fine Arts reached agreements with Italy's Culture Ministry to return numerous antiquities which Italy claimed had been looted.

Reaching an agreement with the Getty has proved far tougher - precisely because, according to an insider in the Culture Ministry, of the ongoing trial, which has introduced an element of antagonism that the two sides have been unable to transcend.

This week the Getty agreed to return 26 objects which Italy claims were looted. The Italians have waived their claim on six more objects, which were in dispute. But that leaves another 20, including Aphrodite, that Italy wants and the Americans have no intention of surrendering.

Last week Giuseppe Proietti, a senior official at the ministry, said: "I will suggest the Italian government takes cultural sanctions against the Getty, suspending all cultural co-operation." Regarding the 26 pieces returning to Italy, Maurizio Fiorilli, a lawyer with the ministry, said: "The pieces will come to Italy not as a concession but as a seizure ... that is part of our legal process."

The Getty's director, Michael Brand, who claimed the museum now has an acquisitions policy "that is the strictest of any North American art museum", said he could only hope for "a change of heart on the Italian side".