It's disappointing, but perhaps not unexpected, that the opening of the new Acropolis Museum was accompanied by bickering over the future of those of the Parthenon marbles that are at the British Museum (BM).

"Neither the trustees nor the British government believe that they should be returned," said a department for culture spokesman, who predictably continued, "I can't imagine that the circumstances will ever change."

The BM did at least have the good grace to "warmly welcome" the opening of the new museum before quickly reminding us that its trustees "remain convinced that the current division" between London and Athens is a good thing.

The Greek government also took a hard line. In response to a suggestion that the marbles could be lent for a short period, Greek culture minister Antonis Samaras fixedly replied: "No Greek government could accept that."

That blunt rejection in part results from the amount of Greek national pride that has been invested in the marbles row. It's also because when lending is mentioned, the BM tends to say that before anything like that could happen, its legal ownership of the marbles would need to be acknowledged, a suggestion guaranteed to send Greek politicians apoplectic.

So much for cultural diplomacy - or any kind of sensible diplomacy, the golden rule of which is surely always to leave yourself a tiny bit of room to wiggle.

The row about the marbles has been going on for about 200 years and the protagonists have got themselves into very tight corners, so a resolution won't come easily. But come it must. I can't decide whether they are best in London or Athens, but I think collaboration and mutual respect would serve the world better than sniping.

Successful international collaborations around once-disputed cultural property show that focusing on legal questions like ownership or on sentimental assertions of national identity aren't constructive. The dialogue needs to be reframed in terms of public benefit, underpinning values and common goals.

Much unites the two museums. They are both committed to education, preservation, research and sharing collections with the people of the world.

The museums could begin to explore ways to cooperate, so building trust. Politicians and officials need to create the conditions of good faith in which this could happen, and give the museums gentle encouragement. They'll need to leave the museums to quietly work together, without prejudging what the long-term results might be.

Resolving the current mess requires the two governments and the two museums to respect each other's constraints, hopes and fears and focus on what unites them, and abandon their outdated assertions of British ownership and Greek nationalism.

Maurice Davies is the deputy director of the Museums Association