Unesco says its destruction would be "an enormous loss to humanity", but no damage has been reported there yet.
IS now control the nearby airport, prison and intelligence HQ, the Syrian Observatory for Human Rights says.
The militants have previously demolished ancient sites in Iraq that pre-date Islam.
The
BBC's Jim Muir in Beirut says acute international concern over Palmyra
might actually spur the jihadists on to make destroying it a priority,
since they delight in challenging and horrifying world opinion.
The
ancient ruins are situated in a strategically important area on the
road between the capital, Damascus, and the contested eastern city of
Deir al-Zour
