At the close of their two-day visit to Greece, German Interior Minister Thomas de Maiziere and his French counterpart Bernard Cazeneuve said authorities need to better coordinate their security databases on Europe's borders.
Data from the passport-free Schengen zone must include "terrorism [records] by police and intelligence agencies, and conditions must be created to link the Schengen system to other criminal records," Cazeneuve told reporters.
The European Union is currently facing its most serious migration challenge since the Second World War, and the issue has brought to light internal divisions which are complicating efforts to implement a united response to the crisis.
Greece, which is handling the bulk of refugee and migrant arrivals from neighbouring Turkey, has pledged to speed up the completion of registration centres known as hotspots after coming under strong criticism from Brussels last month.
The Greek army has been brought in to overcome delays in finishing the hotspots on the five principal Aegean Sea islands that saw over 800,000 arrivals last year.
Greek Defence Minister Panos Kammenos has promised that the hotspots, held up by bureaucratic delays and in the case of Kos island, strong opposition from the locals, will be operational by 15 February.