A diplomatic spat erupted between Greece and the UK on Monday after British Prime Minister Rishi Sunak canceled a meeting with his Greek counterpart Kyriakos Mitsotakis.
It prompted Athens to accuse London of trying to avoid discussing the contested Parthenon Marbles.
The two leaders were due to hold talks at noon on Tuesday in the British capital.
"I would like to express my displeasure at the British Prime Minister's cancellation of our meeting just a few hours before it was due to take place," the Greek PM said in a statement.
The BBC reported that Mitsotakis declined an offer to meet British Deputy Prime Minister Oliver Dowden, as an alternative to his slated meeting with Sunak.
Mitsotakis was due to raise Greece's decades-old demand for the return of the ancient sculptures from the British Museum in London.
"Greece and Britain are linked by traditional bonds of friendship, and the scope of our bilateral relations is very broad," Mitsotakis said. "Greece's positions on the matter of the Parthenon Sculptures are well known. I had hoped to have the opportunity to discuss them with my British counterpart, together with the current major international challenges: Gaza, Ukraine, climate change and immigration. Whoever believes that his positions are well-founded and just is never afraid of engaging in a debate."
"The UK-Greece relationship is hugely important," Sunak's office said in a statement that made no mention of the disputed sculptures. "From our work together in NATO, to tackling shared challenges like illegal migration, to joint efforts to resolve the crisis in the Middle East and war in Ukraine."
The statement added: "The deputy prime minister was available to meet with the Greek PM to discuss these important issues."
What is the Parthenon Marbles row?
Greece has long called for the return of the sculptures that were taken by British diplomat Lord Elgin in the early part of the 19th century.
The sculptures originally adorned the 2,500-year-old Parthenon temple on the Acropolis. However, they have since been displayed at the British Museum for over 200 years.
Around half the surviving marble works, sometimes referred to as the Elgin Marbles, are in London, while the rest lie in a purpose-built museum under the Acropolis.
In March this year, Sunak vowed the UK would not be changing a British law that means it cannot return the Parthenon fragments back to Greece.