"After a quick advance, IS now controls most of the city of Palmyra except the southern part," said Rami Abdel Rahman of the Syrian Observatory for Human Rights.
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"The airport which is outside the city (just to the east) is now surrounded by jihadists."
IS began an offensive just days ago near the town which is on UNESCO's world heritage list.
In May last year, the group seized several towns in Homs province including Palmyra, where they caused extensive damage to many of its ancient sites.
They were ousted from Palmyra in March by Syrian regime forces backed by Russia.