The highest support for more significant EU involvement was seen in Cyprus, Portugal and Italy, all around 90 per cent.
In Austria, Croatia and Poland where support was relatively the lowest, the rate was as high as three quarters, Xinhua news agency reported.
The survey found the perceived threat of terrorist attacks varied from seven per cent in Slovenia to 64 percent in France.
The survey found that the fight against terrorism is an area with an explicit and very strong perception of a gap between the expectations of EU citizens and the actual level of the union's involvement -- 69 per cent considered the current EU involvement to be insufficient.
Eurobarometer said measures perceived as the most urgent were blocking the financing of terrorist groups, studying the roots of terrorism and radicalisation, and strengthened control of external EU borders.
The European Parliament argued that under the existing legal framework, there is still some scope for further developing EU counter-terrorism capacities.
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