Potential terrorists are taking advantage of failing European Union border control checks, the EU's border agency has warned.
Frontex said a large number of people arriving mainly in Greece and Italy with false documents are not facing thorough checks or penalties.
It said the Paris attacks last November demonstrate irregular migration patterns could be used by terrorists to reach the EU.
Meanwhile, it revealed more than 1.8 million illegal border crossings were detected by EU member states in 2015, six times the number reported in 2014.
The agency said the never-seen-before figure is still linked to the estimated one million individuals who reached the EU, suggesting many crossed two sections of the external borders of the EU.
The report, Risk Analysis for 2016, said: "The Paris attacks in November 2015 clearly demonstrated that irregular migratory flows could be used by terrorists to enter the EU.
"Two of the terrorists involved in the attacks had previously irregularly entered through Leros and had been registered by the Greek authorities. They presented fraudulent Syrian documents to speed up their registration process.
"As the vast majority of migrants arrive undocumented, screening activities are essential to properly verify their declaration of nationality.
"With a large number of persons arriving with false or no identification documents or raising concerns over the validity of their claimed nationality - with no thorough check or penalties in place for those making such false declarations, there is a risk that some persons representing a security threat to the EU may be taking advantage of this situation."
The report added that there is no EU system capable of tracing people's movements following an illegal border-crossing, so it is therefore impossible to establish the precise number of people who have illegally crossed two sections of external EU borders.
"Only an estimate of about one million persons can be provided, based on the assumption that all migrants first detected irregularly crossing in Greece were then detected for a second time re-entering the EU from the Western Balkans," the report said.
"The unprecedented number of detections of illegal border-crossing has also led to a surge in violent incidents along the EU's external borders.
"People smugglers, motivated by profit, increasingly put migrants' lives at risk and even threaten border guards to recover boats or escape apprehension."
It said EU citizens who had joined Islamic State in Syria were taking advantage of the irregular migrations flows to return home.
The report said: "The staggering number of EU citizens who joined the conflict as jihadists has resulted in a number of returnees opting to use irregular means of travelling.
"Islamist extremists will exploit irregular migration flows whenever such movements' fit their plans."
The report was seized on by campaigners wanting to leave the EU, who said the UK was at risk from terrorists able to slip through European borders.
A Leave.EU spokesman said: "Prevented by free movement rules from carrying out extensive background checks on EU nationals, we are now in clear danger from European Islamists, who can seek to establish UK terror cells after slipping through the Schengen Area's porous external border.
"Incredibly, the EU's only answer to what has become a full-blown security crisis is to propose an armed European Border and Coast Guard, directed from Brussels and capable of seizing control of member countries' frontiers without their permission."