The 2,500 year-old marble sculptures were brought over to Britain in the early 19th century and bought by the Government who passed them on to the British Museum where they remain one of the most prized exhibits.
Ministers have long-resisted calls for the classical sculptures to be returned to Greece.
SNP defence spokesman Brendan O’Hara used a discussion in the House of Commons on the Cultural Property (Armed Conflicts) Bill - which enshrines greater protection for historic artefacts on conflict zones - to reignite the debate.
He said: “In the spirit of the Convention, we would urge that the Government take this opportunity to return the Parthenon Marbles, the Elgin Marbles, to Greece where they belong.
“The passing of this bill and the ratification of these protocols provide this Government with an excellent opportunity to lead by example and celebrate the ratification of this Convention with the highly appropriate and long-overdue gesture.”
Tory former culture minister Ed Vaizey accused the SNP of doing the bill a “great disservice” by linking it to the row about the Elgin Marbles.
And he defended their home in the British Museum, which they are kept in “pristine condition” free for the world to view.
He said: “The Elgin Marbles were purchased legitimately in the 19th century.
“But not only that they have been preserved to the very highest standards possible in the greatest museum in the world, which is a world museum open to all free of charge, where the Elgin Marbles are seen in pristine condition by millions of people and indeed were recently loaned and sent to Russia for even more people to see.
“The British Museum preserves the Elgin Marbles not for any nationalist self-interest, but for the world.”
Lord Elgin removed the sculptures from the site where they stood on the Acropolis in Athens.
Many say they should be returned to Athens where they can be reunited with the rest of the Parthenon.
A law proposed by Lib Dem Mark Williams forcing Britain to return the Elgin Marbles to Greece is tabled to get a second reading in January, but is unlikely to be heard because of a lack of parliamentary time.