At least 23 regime loyalists and 29 jihadists were killed as IS overran northern neighbourhoods of the adjacent modern town of Tadmur late yesterday, the Syrian Observatory for Human Rights said.
The Britain-based watchdog reported heavy artillery exchanges in the west of the town, close to the UNESCO-listed world heritage site.
But Syrian antiquities chief Mamoun Abdulkarim said clashes had subsided by mid-morning as troops pushed IS out of the northern part of the adjacent modern town of Tadmur.
"There was no damage to the ruins, but this does not mean we should not be afraid," Abdulkarim added.
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IS had brought up reinforcements from its stronghold in the Euphrates Valley to the east after sustaining heavy losses in its advance on the oasis town northeast of Damascus, provincial governor Talal Barazi told AFP.
The town's peacetime population of 70,000 has been swamped by an influx of civilians fleeing the IS advance.
"We are taking all necessary precautions, and we are working on securing humanitarian aid quickly in fear of mass fleeing from the city," Barazi said.
The antiquities chief said he had been "living in a state of terror" that IS would destroy Palmyra's well-preserved architecture, regarded as one of the jewels of the ancient Middle East.