The shrines of prophets Daniel and Jonah, which have significance for Jews as well as Christians and Muslims, are believed to have been destroyed.
Iraqi media reported a month ago that unspecified militants had taken over a synagogue in Amarah, south of Baghdad, causing widespread damage and turning the building into their headquarters. And a third-century synagogue at Dura-Europos in eastern Syria is believed to be in the hands of IS and in danger of being destroyed.
However, Dr Vukosavovic said he believed that cases of known harm were just the tip of the iceberg, and that the extent of the damage was unthinkable.
"Who cares about a synagogue where there are no more Jews?" he asked rhetorically.
Shmuel Moreh, chairman of the Israel-based Association of Jewish Academics from Iraq, agreed with this assessment. He said that locals who witness destruction keep quiet and it is therefore difficult to know. His contacts on the ground are now "very scared" to send him information. Dr Moreh has lobbied and visited the United Nations Educational, Scientific and Cultural Organisation to urge its intervention.
Bar Ilan University archaeologist Aren Maier was more worried about artefacts than sites. In the case of IS, he said: "It's much more than just destroying culture - they are destroying whatever they can't sell." He reported that the antiquities market was "flooded" with illicit excavations from Iraq and Syria, many of which were carelessly dug up, often causing damage to other artefacts, and sold by militants to raise money for arms.
Artefacts of Jewish interest that have come from these areas in the past have included information about Jews exiled there and Jewish-written documents from the time of the Babylonian Talmud, which was written in what is now Iraq.
"Mesopotamia is one of the richest areas from an archeological point of view and there is so much to be found there and so much to be destroyed, so it's a very sad time," said Dr Maier.
Dr Vukosavovic, whose historical interests are general as well as Jewish, commented: "I have a PhD in the ancient history of Iraq and would like to go there and excavate, but I am devastated that, if you go in a few years, there would be nothing left."
