Europol said this week that the terror group is determined to continue attacks against EU members and could deploy methods that have been successful in Syria and Iraq, including "car bombs, extortion and kidnappings".
"France remains high on the target list for IS (ISIS) aggression in the EU, but so too do Belgium, Germany, the Netherlands and the UK," the report says.
"Estimates from some intelligence services indicate several dozen people directed by IS may be currently present in Europe with a capability to commit terrorist attacks, and that there are indications that IS has been preparing for terrorist attacks in Europe since 2013," it adds.
"Those who manage to enter the EU will pose a potential security risk for the Union. Given the high numbers involved, this represents a significant and long-term security challenge," the report warns.
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The report also warned of "a real and imminent danger" of IS trying to recruit Syrian refugees into jihadism once they reached Europe.
"A real and imminent danger is the possibility of elements of the (Sunni Muslim) Syrian refugee diaspora becoming vulnerable to radicalisation once in Europe and being specifically targeted by Islamic extremist recruiters. It is believed that a number of jihadists are travelling through Europe for this purpose," it said.
Europol said that IS appeared to remain focused on "soft targets", lightly-guarded places where there were large numbers of civilians to kill, rather than more difficult targets like power grids or nuclear facilities.