EU leaders believe that stricter border controls need to be imposed in the Shengen area.
At a meeting in Brussels on Thursday they agreed to tighten measures to "disrupt terrorist travel".
Checks against anti-terrorism databases would be carried out on "individuals enjoying the right of free movement".
The Shengen agreement abolished internal borders, allowing passport-free movement between 26 European countries, excluding the UK and Ireland.
Rather than revising the current agreement, steps could be taken within it to monitor travellers entering or leaving the zone without undermining the right to free movement.
Countries would "proceed without delay to systematic and co-ordinated checks'' on anyone whose movements are flagged as suspicious by databases that use unspecified "common risk indicators", the statement said.
Currently, just about 30% of passports of those entering or leaving Shengen borders are checked electronically to see if they are counterfeit or stolen or reported lost.
The leaders also called for police to increase information sharing.
Some of the measures will need approval by the European Parliament to go into effect.
Comments
"The right to free movement" is a strange concept, since it has only ever applied to those with the documented right to enter the EU.