The Islamic State militants had overrun much of the north of Tadmur after fierce clashes with government forces, activists say.
Syria’s head of antiquities Maamoun Abdul Karim said the world had a responsibility to save Palmyra, a UNESCO World Heritage site.
Hundreds of statues had been moved to safety, but large monuments could not be moved, Maamoun Abdul Karim warned.
ISIS militants have ransacked and demolished several ancient sites that pre-date Islam in Iraq, including Hatra and Nimrud, leading to fears that it might attempt to damage or destroy Palmyra.
On May 20, the Syrian Observatory for Human Rights said a third of Tadmur had been taken by ISIS after battles with government soldiers and allied militiamen.
Rising out of the desert and flanked by an oasis, Palmyra contains the monumental ruins of a great city that was one of the most important cultural centers of the ancient world, according to UNESCO.
The site, most of which dates back to the 1st to the 2nd Century when the region was under Roman rule, is dominated by a grand, colonnaded street.
Palmyra and Tadmur are situated in a strategically important area on the road between the capital, Damascus and the contested eastern city of Deir al-Zour, and close to gas fields.
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