The militants are now in control the nearby airport, prison and intelligence HQ, according to the Syrian Observatory for Human Rights.
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.
UNESCO, Director-General, Irina Bokova said: "We need indeed to have the Security Council, we need to have, all political leaders, we need very much the religious leaders also to launch an appeal of the prevention of this destruction."
Rising out of the desert, the site contains the monumental ruins of a great city, which UNESCO and others consider one of the most important cultural centres of the ancient world.
Dating back to the 1st and 2nd Century, when the region was under Roman rule, Palmyra is dominated by a grand, colonnaded street.
