The UK prime minister reportedly called off the Tuesday lunchtime meeting with Kyriakos Mitsotakis just hours before it was meant to take place.
A senior Conservative source told the BBC that the meeting was “impossible” after Mitsotakis publicly commented on the marbles, suggesting that went against a previous agreement between Greece and the UK.
Mitsotakis did manage to squeeze in a meeting with Labour leader Keir Starmer before the row with Sunak unfolded.
Also known as the Parthenon Sculptures, the famous statues are currently held in the British Museum.
The UK says handing them back would be a breach of a 1936 law which prevents objects being removed from the institution.
The PM’s spokesperson said: “There are no plans to change our approach, we believe the museum is the right place for them. He has been fairly robust on his position. We have cared for the marbles for generations and we want that to continue.”
But, Greece argues that, as the marbles were taken from a 2,500-year-old temple in Athens in the early 19th Century by British soldier and diplomat Lord Elgin, they ought to be returned to their rightful home.
Social media has not been sympathetic to Sunak’s side of the story, with many criticising his last-minute rescheduling.