Rishi Sunak has said there are "no plans" to change a law which prevents the permanent return of the Elgin Marbles to Greece.
The sculptures - also known as the Parthenon sculptures or marbles - were controversially removed from one of the world's most historic monuments in Athens by British diplomat Lord Elgin in the early 19th century and shipped to the UK.
In January, there were reports the British Museum was drawing up an agreement with Greece to loan back the Elgin Marbles in a long-term "cultural exchange".
British Museum chairman George Osborne, the former chancellor, has reportedly been a driving force behind the effort, by exploring ways for the sculptures to be displayed in Greece.
Sunak's comments to journalists appear to put him at odds with his fellow Tory.
The 1963 British Museum Act prevents the institution from giving away objects from its collection, except in very limited circumstances.
Sunak says museum's treasures 'shared with the world'
Speaking to reporters during a trip to San Diego in the US, Mr Sunak said: "The UK has cared for the Elgin Marbles for generations.
"Our galleries and museums are funded by taxpayers because they are a huge asset to this country.
"We share their treasures with the world, and the world comes to the UK to see them.
"The collection of the British Museum is protected by law, and we have no plans to change it."
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How the Elgin Marbles ended up in the UK
Amal Clooney calls on UK to return sculptures
The Parthenon Project, which has been backed by MPs from different political parties to settle the issue, said on Sunday the British Museum's Parthenon collection could be returned to Greece under a long-term cultural partnership agreement.
Decisions about the care and management of specific collections are a matter for the museum and its trustees.
Since independence in 1832, Greece has repeatedly called for the return of the sculptures.
Lord Elgin, who was the ambassador to the Ottoman Empire which then ruled Greece, oversaw the removal of the sculptures from the Parthenon temple in Athens as part of a lengthy operation which started in 1801.