Diners at a fish taverna in Thessaloniki on Saturday night could have been forgiven for thinking they had seen the spirit of Alexander the Great hovering over their tables. The warrior king’s cultural pedigree and historical reach were certainly on the minds of those present.

This was no ordinary meal – either for Yiannis Boutaris, Thessaloniki’s mayor or his guest Zoran Zaev, prime minister of the former Yugoslav republic of Macedonia. The two were sending a signal: that old enmities belonged to the past, along with the nationalist rhetoric that for more than a quarter of a century has kept Greece and its northern neighbour at loggerheads.

“I am not expressing national diplomacy or strategy,” Boutaris told the Observer. “But I do think this bullshit has to end.”

The dispute erupts intermittently over an issue that boils down to identity. In each reprise the focus, invariably, is on Alexander the Great – and who can rightly claim him as their own – and the thorny question of what to call the multi-ethnic mini-state.

In Athens, “republic of Macedonia” is unacceptable because it is seen as implying irredentist ambitions against the adjacent Greek province, which bears the same name. In Skopje, the republic’s capital, officials have long argued they have a historical right to a name now enshrined in the state’s constitution.

Whether viewed from the aspect of cultural theft or nomenclature, the feud remains as bitter as it is abstruse. On both sides there are those who argue fervently that as exclusive heirs to Alexander’s legacy, Macedonia belongs to them.

But Zaev’s decision to spend New Year’s Eve in Thessaloniki is further evidence that emotions are changing. And, say officials in Greece’s leftist-led coalition, proof that a row that reputedly had once put the neighbours on a war footing – and as of 2008 blocked Skopje’s entry to Nato and the EU – will soon be settled. “It is a silly [dispute] that has to be solved,” confided the interior minister Panos Skourletis, a prominent figure in the ruling Syriza party. “They want to solve it and I think it will be solved in 2018. If not now, then when?” Skourletis has reason to be optimistic. In a TV interview before Christmas, Zaev said his social democrat government was ready to concede ownership of the man who ruled the ancient kingdom of Macedonia. “I give up the claim of Macedonia being the sole heir to Alexander. The history belongs not only to us, but also to Greece and many other countries,” he said, referring to Macedonia’s geographical spread.

Zaev has also denounced a mammoth statue and building campaign that inflamed passions under his nationalist predecessor, Nikola Gruevski. The programme has named the nation’s airport, highways and stadiums after the warrior king, fuelling accusations in Athens that the country is stealing symbols and heroic personalities from ancient Greece to buttress its claim to the name. Since assuming office in June, the Zaev government has suggested it will dismantle statues that have offended Greeks.

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Realpolitik and fears of Russian meddling in the Balkans appear to have taken precedence. The row has been the biggest obstacle to impoverished Macedonia’s integration with the west. Fervently pro-European, Zaev has made EU accession a priority. Greece, itself in economic crisis for the best part of decade, also stands to gain if stability is restored to the region.

In what was seen as a major compromise, Athens has announced it will accept a composite name in which the word Macedonia can feature. Mooted name changes have included adding geographic qualifiers such as “upper,” “new” or “northern” Macedonia. For the most part, Greeks insist on calling the country the former Yugoslav Republic of Macedonia (Fyrom) and its two million population “Skopjian”.

Twenty five years ago Thessaloniki saw more than a million citizens take to the streets chanting “Macedonia is Greek!” Now the city welcomes their Slav neighbours as tourists. “For too long we have been obscured by this nationalistic foolishness and populist propaganda,” says the mayor. “I will take Zaev to the best fish taverna, and no doubt Alexander the Great will be part of the conversation, but my priority will be to ensure that, as my guest, he has a great time too.”