The surveys also suggest that support for the European Union's priorities and policies remains strong, and has increased since spring 2016.
These are two key results of the latest Standard Eurobarometer survey published on Thursday, together with the Special Eurobarometer survey, “Future of Europe”.
Asked about their main concerns, immigration remains on top of the issues facing the EU most frequently cited by citizens (45 per cent,-3 percentage points since spring 2016).
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Terrorism (32 per cent,-7) remains the second most frequently cited item. It is well ahead of the economic situation (20 per cent,+1), state of member states' public finances (17 per cent, +1) and unemployment (16 per cent,+1).
Immigration is number one concern for the EU in all member states, except Spain and Portugal.
At national level, the main concerns are unemployment (31 per cent,-2) and immigration (26 per cent,-2). The economic situation is in third place (19 per cent, unchanged).
Compared to the previous survey of spring 2016, support for the priority topics set by the European Commission has increased further, the surveys say.
Regarding the issue of migration, 69 per cent of Europeans say they are in favour of a common European policy on migration and 61 per cent are positive about migration of people from other EU member states. However, 56 per cent are negative about immigration of people from outside the EU.
Some 81 per cent of Europeans are in favour of the "free movement of EU citizens who can live, work, study and do business anywhere in the EU".
Majorities of respondents support free movement in all countries.