Palmyra's UNESCO-listed heritage site, including ancient temples and colonnaded streets, and its adjacent museum housing priceless artefacts, are in the city's southwest.
"The situation is very bad," said Syria's antiquities chief, Mamoun Abdulkarim.
"If only five members of IS go into the ancient buildings, they'll destroy everything," he added, calling for international action to save the city.
The head of the UN cultural agency, Irina Bokova, demanded an immediate halt to fighting in Palmyra which was "putting at risk one of the most significant sites in the Middle East".
It was the second time IS has overrun northern Palmyra, after it seized the same neighbourhoods on Saturday but held them for less than 24 hours.
Rami Abdel Rahman of the Syrian Observatory for Human Rights said IS had seized roughly "a third" of Palmyra.
After fierce clashes on the city's edges, the jihadists entered the northern quarter on foot and seized a state security building before fanning out as regime forces fled.
The jihadists sparked international outrage earlier this year when they blew up the ancient Assyrian city of Nimrud and smashed artefacts in the Mosul museum.
Asked if IS would be able to reach Palmyra's ruins, a Syrian military source said "everything is possible in urban warfare".
The source acknowledged the jihadists had infiltrated northern neighbourhoods and said they were engaged in "street fighting".
Mohammad Hassan Homsi, another activist originally from Palmyra, said the fleeing regime soldiers "headed to the military intelligence headquarters near the ruins".
The jihadists' capture of the city was their most significant victory since mid-2014 when they conquered swathes of land, sparking a US-led air campaign to support Baghdad.
The United States says it is now considering accelerating the training and equipping of tribal forces to fight IS following Ramadi's fall.
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