Manuel Navarrete Paniagua, counterterrorism chief for Europol, the EU's law enforcement agency, told members the European Parliament Committee on Civil Liberties that "secondary checks at the member state level, especially in Greece and Italy," are essential.
"We have some information reported by the member states that terrorist groups are trying to establish large clandestine stockpiles of explosives in the European Union to be used eventually in large scale home attacks," Paniagua said during a recent debate.
The same people forced by terrorists to flee their country and become refugees are being exploited by terrorists who are now "using them to infiltrate the EU," according to Paniagua, who told MEPs he had heard unconfirmed reports that Daesh militants have established training camps in the Western Balkans and EU member states.
Paniagua told MEPs that Europol officers have been deployed at hotspots on four Greek islands and on Sicily to spot potential terrorists.
"However, member states are in charge and they decide what to do with any suspects."
There is no specific data on the number of terrorists who have infiltrated the European Union through migration flows, but Paniagua says Europol is aware "that they are doing so."
'Fragmentation Makes Us Vulnerable'
Meanwhile, concerns remain over the number of so-called homegrown jihadists who have fled Europe to Iraq and Syria to train with extremists with the intention of returning to Europe to carry out terrorist-related attacks.
According to a report in German newspaper Die Welt, only 2956 EU citizens have been registered by Europol as having travelled to Iraq or Syria to become of foreign fighters; but the number is more like 5,000.
During a recent meeting of European interior ministers in Luxembourg, Dimitris Avramopoulos, EU migration, home affairs and citizenship commissioner said that the gap in the figures suggested that not all member states are feeding enough information into the common database, allowing "dangerous individuals to get away without being detected."
Avramopoulos said there are too many different EU databases which are not linked up into one system and suggested that there should be just one database to exchange information among member states.
"Fragmentation makes us vulnerable," Avramopoulos said.
It's estimated that 6,000 people from Europe have becoming foreign fighters in Iraq and Syria; the majority of them leaving France, Germany and the UK.