Directorate of Syrian Antiquities shows damage to city's museum and the Temple of Bel.
The military is reportedly just hundreds of meters from the city's ancient sites.
The pop star, 21, was asked to leave a Mayan site in Tulum, Mexico.
The Islamic State militant group demolished artefacts for "idolatry" in Palmyra in 2015.
A shipment of a few hundred small clay tablets from Iraq in 2011 might have been illegal.
Archaeologists believe the discovery could lead to an ancient ritual site, or the tomb of a king.
Zeno, Epictetus, Seneca and Marcus Aurelius, the great Stoic philosophers of the classical world, are back in vogue
While they were excavating a tomb in northern Greece, a 10-by-15-foot mosaic appeared
Two "matching" towns from the Basketmaker period were discovered in neighboring sand dunes