Malmström called for closer cooperation and stronger national strategies to prevent extremist groups and to encourage them to abandon violence.
Commenting on the report, terrorism expert Magnus Ranstorp of the Swedish National Defence College, told Radio Sweden: "It's a comprehensive, holistic initiative and builds on the work that Malmström launched with the Radicalisation Awareness Network in 2011."
Ranstorp said that when it comes to extremism, different EU countries face different problems today, but that there is generally a resurgence of right-wing extremism in the political realm as well as violent right-wing extremism.
"We are also seeing, in the wake of the financial crisis, a resurgence in left-wing extremism," said Ranstorp. "And perhaps the most important issue for security services across Europe is the foreign fighter issue in Syria, with European nationals traveling to Syria to participate in Al-Qaeda-affiliated groups."