By Henry Zeffman, Harrison Jones & Chris Mason, BBC News
UK Prime Minister Rishi Sunak cancelled his meeting with the Greek prime minister after it was felt a promise not to publicly discuss the Parthenon Sculptures was broken, Downing Street said.
Kyriakos Mitsotakis told the BBC on Sunday he wanted the artefacts - also known as the Elgin Marbles - returned from the British Museum to Greece.
The meeting was scrapped on Monday at late notice.
A Greek government source denied assurances were given to the UK.
They said discussions preparing for Tuesday's meeting with the UK PM had been smooth until late afternoon on Monday - long after Mr Mitsotakis's BBC interview with Laura Kuenssberg on Sunday.
In the interview, Greece's leader said having some of the treasures in London and others in Athens was like cutting the Mona Lisa in half.
But the PM's official spokesman said on Tuesday that when the meeting was requested "the Greek government provided reassurances that they would not use the visit as a public platform to relitigate long-settled matters relating to the ownership of the Parthenon Sculptures" - arguing those assurances were then "not adhered to".
The spokesman told reporters Sunak had decided it would "not be productive" to hold the meeting.
Labour has described the row as "petty" and "small-minded".
The sculptures are a collection of ancient Greek treasures from the Parthenon in Athens which were taken and brought to the UK by British diplomat Lord Elgin in the early 19th Century.
They have been in the British Museum since 1832, aside from a stint in Aldwych Tube station during World War Two to prevent damage and one marble being loaned to a Russian museum in 2014.
Both Greece and the UK have long-standing positions on the sculptures, but diplomatic talks were expected to focus on other topics.
Transport Secretary Mark Harper told BBC Breakfast on Tuesday it was a "matter of regret" that no meeting would take place between the two countries after Mitsotakis declined a secondary offer to meet Deputy Prime Minister Oliver Dowden instead.
Asked whether the government's treatment of the Greek leader was rude, Harper said the Greeks had been offered a senior-level meeting but were entitled to take their own view.
A Greek minister branded the row a "bad day" for British-Greek relations.
Adonis Georgiadis told BBC Radio 4's World at One programme that Sunak's decision had been a "mistake".
Stressing his "huge respect" for the British people and the two countries' friendship, the minister of labour and social insurance said: "What [the Greek PM] mentioned in his interview is not just his own opinion, it is the single one opinion of 11 million Greek people."
Professor Irene Stamatoudi, a former member of the advisory committee for the Greek Minister of Culture, said the row "makes Rishi Sunak look no better than Lord Elgin" - and accused that diplomat of smuggling artefacts "to decorate his country house in Scotland".
She told Today it was "not possible" for the Greek PM not to respond to questions about the Parthenon Sculptures.
Sunak is keen to be seen as a defender of the marbles' place in London. A senior Conservative source said: "Our position is clear - the Elgin Marbles are part of the permanent collection of the British Museum and belong here."
Later on Tuesday, the PM's official spokesman told reporters Sunak had decided it would "not be productive" to hold the meeting.
He said that when the meeting was requested "the Greek government provided reassurances that they would not use the visit as a public platform to relitigate long-settled matters relating to the ownership of the Parthenon Sculptures" - arguing those assurances were then "not adhered to".
Mitsotakis had told reporters on Monday evening he was "deeply disappointed by the abrupt cancellation" of the talks, which had been planned for Tuesday lunchtime.
Sources with knowledge of the mood in the Greek government have suggested Mitsotakis was both "baffled" and "annoyed".
In his interview with Laura Kuenssberg the day before, the Greek PM had called for the sculptures to be returned.
He said they were "essentially stolen" and called for a partnership with the British Museum so people could "appreciate" the works "in their original setting".
Mitsotakis met Labour leader Sir Keir Starmer on Monday and will return to Greece later after other scheduled meetings.
On Tuesday morning, Greek government spokesperson Pavlos Marinakis told SKAI TV that "Britain's attitude shows no respect for the prime minister and our country".
He added that although cancelling a meeting was not "common", the Greek government did not want "to escalate the issue with a country with which we have good relations."
There is an ongoing wider debate around the place of museums and their collections in a post-colonial world, with Sunak seemingly positioning himself decisively on one side of that argument.
Lord Vaizey, who chairs the advisory board of the Parthenon Project dedicated to returning the Elgin Marbles to Greece, told the Today programme it was "odd" for the PM to cancel the meeting.
The ex-culture minister said: "It is tied up to a certain extent in the traditional culture wars, where anyone who dares to say that British history wasn't perfect is somehow unpatriotic.
"The trouble with that is that, from what I can gather, every opinion poll that surveys the British public says that they do think that the sculptures should be returned."
Thangam Debbonaire, Labour's shadow culture secretary, said it was "petty" and "small-minded" to cancel the meeting, and called Sunak "reckless".
"To have decided to create division where none needed to be seems to me to be not just reckless but actually potentially really damaging to our international reputation," she added.
Labour is also distancing itself from reports in a Greek newspaper suggesting it was open to "a legal formula" for the return of the sculptures to Greece.
Instead, the party says its position is that if the British Museum and the Greek government came to a loan agreement, a Labour government would not stand in the way.
A spokesperson for the UK government said there were "no plans" to change the 1963 British Museum Act - which prohibits the removal of objects from the institution's collection.
But a loan does not require a change in the law and so could happen irrespective of any PM's position.
Unesco, a UN agency which was established to promote world peace and security through cooperation on arts and culture, has told the BBC it "stands ready" to broker an agreement between the UK and Greece, "if they express the desire for such support".
What are the Parthenon Sculptures, also known as the Elgin Marbles?
- Friezes and pediment figures which decorated the Parthenon temple in Athens, built 447-432 BC
- The Marbles taken to Britain include about a half (some 75 metres) of the sculpted frieze that once ran all round the building, plus 17 life-sized marble figures
- Most of the surviving sculptures are roughly equally divided between London and Athens
- The new Acropolis Museum opened in Athens in 2009. It is designed to display all the surviving sculptures, in their original layout
- Celebrities previously involved in the campaign for their return include the late actress and former Greek Culture Minister Melina Mercouri
- Art lover Lord Elgin claimed the sculptures were better off in Britain than the then-dilapidated Parthenon
- In 1801, he negotiated what he claimed was permission from the Ottoman Empire - which then controlled Athens - to remove statues from the classical temple built by the Ancient Greeks - and caused some damage to the ruin in doing so
- Fragments from the Parthenon alone ended up in some 10 European countries, or were lost altogether
- This story was first published by the BBC.