"It's as though there is a curse that has befallen this city and I expect only news that will shock us. If the city remains in their hands the city is doomed," Syria's antiquities chief Maamoun Abdulkarim told Reuters on Sunday.
"It is now wanton destruction... their acts of vengeance are no longer ideologically driven because they are now blowing up buildings with no religious meaning," he added.
In August, the Sunni Muslim militants blew up the temple of Baal Shamin, then the Temple of Bel, one of the best preserved Roman-era sites.
Earlier this month it was also confirmed the militants had destroyed some of the best preserved of Palmyra's funeral towers, sandstone constructions built to hold the remains of the ancient city's richest families.
Palmyra was one of the most important cultural centers of the ancient world, according to cultural agency UNESCO, which has described it as the crossroads of several civilizations.
Islamic State has declared a caliphate in territory it holds across Syria and Iraq and has destroyed other monuments it says are pagan and sacrilegious.
UNESCO has called such acts war crimes and says Islamic State seeks to wipe out evidence of Syria's diverse heritage.
Before the capture of the city, Syrian officials said they had moved hundreds of ancient statues to safe locations.