"Extremists don't destroy heritage as a collateral damage, they target it systematically to strike societies at their core," Irina Bokova said in a speech at the Chatham House think tank in London.
"This strategy seeks to destroy identities by eliminating heritage and cultural markers," she said.
Several archaeological sites have been attacked by Daesh jihadists in Iraq and Syria and their recent takeover of an area including the ruins of the ancient city of Palmyra in Syria sparked worldwide concern.
In April, the IS group released a video in which militants can be seen using rifles and sledgehammers to destroy artefacts at Hatra.
Earlier the militants also damaged the site of Iraq's ancient Assyrian city of Nimrud and destroyed dozens of pieces from the museum in Mosul.
"I think the growing awareness that hard power will not be enough to defeat violent extremism is gaining ground. We need also soft power," Bokova said.
"Culture should be part of our response to violent extremism," she said.
The organisation has launched a campaign entitled "Unite4Heritage" to defend historical sites under threat from jihadists and counter militant propaganda.