Ministers have been warned that shame is being heaped on the UK because the British Museum is "parading stolen booty" belonging to the Greeks.
Liberal Democrat Andrew George insisted the government needed to work with their Greek counterparts and take the "gracious act" of returning the Parthenon Sculptures to Athens.
A team of London lawyers, including Amal Clooney, have been involved in talks with the Greek government about a potential legal bid for the works, known as the Elgin Marbles. Words: PA
The marble sculptures, which for more than 2,000 years decorated the Parthenon temple on the Acropolis, were removed more than two centuries ago by Lord Elgin, a Scottish nobleman, and are displayed in London's British Museum.
Greece maintains they were illegally removed during Greece's Turkish occupation and should be returned for display in a new Athens museum. However, the British Museum and the British Government reject this.
Speaking in the Commons, St Ives MP Mr George said: "I'm sure if the UK is confident in its position it will willingly engage with Unesco in the offer of mediation.
"Although some others perhaps delude themselves otherwise, the fact is parading stolen booty in the otherwise excellent British Museum is something which I think brings shame on this country.
"Surely the United Kingdom now needs to engage constructively and to engage also in a gracious act and recognise that the Parthenon Sculptures should return to Athens."
Culture minister Helen Grant replied: "We are engaging constructively, we will of course respond to this offer in due course - the suitability, objectives and benefits, of course, of mediation need to be considered before that point.
"But I would repeat again that the sculptures are the property of the British Museum, who provide access to all free of charge."
Labour's Jeremy Corbyn, MP for Islington North, told Ms Grant the items were "stolen from the people of Greece", adding the UK's relations with Greece could be improved if constructive talks took place about returning some or all of the items.
Ms Grant replied: "I don't accept that the items were stolen but I would assure you there is constructive engagement happening between the UK Government and the Greek government.
"The matter was discussed very recently at the beginning of October at Unesco HQ in Paris."