The collection of stone objects, inscriptions and architectural features includes sculptures from the Parthenon in Athens, which were "acquired" by Thomas Bruce, the seventh Earl of Elgin, between 1801 and 1805.
The Earl of Elgin spent £70,000 of his own money—the equivalent of almost $500 million today—to purchase half of the surviving 5th century BC sculptures and then transported them by sea to Britain.
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The U.K. government bought them from him in 1816 and gave them to the British Museum, where they have remained ever since.
Greece has been demanding the return of the spectacular works or more than 30 years but they recently declined to follow the suggestions of a 150-page report prepared by human-rights lawyer Amal Alamuddin, which suggested they take their claim to the International Criminal Court.
Greece "has a just cause and it is high time for the British Museum to recognize this and return them," said Alamuddin, who is the wife of actor George Clooney. However, she acknowledged that Greece only had about a 15 percent chance of winning such a case.
Earlier this year, the British Museum turned down a proposal by UNESCO to mediate in the dispute. It justifies the decision to keep the Parthenon Marbles by claiming on its website that displaying them in London allows the worldwide "public to re-examine cultural identities and explore the complex network of interconnected human cultures." The museum declined to comment when contacted by NBC News on Wednesday.
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Many have also argued that Lord Elgin actually saved the sculptures from ongoing destruction.
The Greek church smashed up a large number of the ancient temple's carvings in the 5th century and the Venetians then blew up chunks of the building in 1687 and in the 19th century. When Lord Elgin arrived in Athens to serve as ambassador, the occupying Ottomans were grinding the sculptures up for limestone and using them for artillery target practice.
"Perhaps Elgin did save them," said Eddie O'Hara, the chairman of the British Committee for the Reunification of the Parthenon Marbles. "But that's a bit like taking someone's washing in because it's raining and not giving it back."
However, one former British lawmaker said it would be "foolish, on an impulse of misguided post-imperial revisionism, to undermine the world's great collections" including the Parthenon Marbles at its current home.
Calling the Smithsonian in Washington, D.C., the Louvre in Paris and Toronto's Royal Ontario Museum as "places of big ideas" in an article for The Guardian newspaper, Alan Howarth wrote: "The major museums have always promoted the cultures of other nations by showing and sharing them in an international and historical context."
Howarth, a former education minister in the U.K. Parliament, added that he could "see a certain force in the argument where if there are countries where removable objects are at risk there would be case for secure museums offering a place of refuge for them."
But that suggestion isn't an option for the ruins of ancient Palmyra.
Al-Azm, the Ohio-based academic who is also former head of the Center for Archaeological Research at the University of Damascus, said that ISIS relished highlighting how "impotent" the international community is to stop their "acts of violence and atrocities."
He added: "One must remember that one day this conflict will end and when it does Syrians are going to have to reach out and look for any common denominators. I think the shared common history and heritage that almost all sides recognize as their own ... will help people come across this great divide which has opened up within Syrian society, and maybe help them reconcile with one another and move on. In a way, saving Syria's past is also saving Syria's future."
NBC News' Sarah Burke and Reuters contributed to this report.