The Islamic State group has ravaged ancient archeological sites under its control in Syria and Iraq, along with local looters. Among the worst incidents was the destruction by IS of temples in the famed ancient city of Palmyra, which provoked international outrage.
"These import restrictions are intended to reduce the incentive for pillage to better preserve Syria's cultural heritage and to combat profiting from the sale of these artifacts by terrorists and criminal organizations," the US State Department said.
"Preserving the cultural heritage of Syria will be a vital component in shaping a future for the country based on reconstruction, reconciliation and building civil society."
The restrictions were published by US Customs and Border Protection, the Department of Homeland Security and the Treasury Department.
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They apply to any cultural property "unlawfully removed" from Syria from March 15, 2011, when the conflict began. This includes objects of stone, metal, ceramic, clay and faience objects, wood, glass, ivory, bone and shell, plaster and stucco, textile, parchment, paper and leather, paintings and drawings, mosaic and writing.
In the IS group's extreme interpretation of Islam, statues and shrines amount to idolatry and must be destroyed.
But the group is also believed to have benefited from the trafficking of antiquities seized from sites under its control.
In Syria, more than 900 monuments and archeological sites have been affected, damaged or destroyed by the regime, rebels or jihadists since the conflict began in March 2011, according to the Association for the Protection of Syrian Archeology.
Between 2014 and 2015, Syria's antiquities department moved some 300,000 objects and thousands of manuscripts from across Syria into storage in Damascus.