Potential terrorists are exploiting the migrant crisis to travel unchecked through Europe, 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 that could be used by terrorists to reach the EU.
It also warned that radicalised EU citizens returning from the Syria conflict are taking advantage of the poor quality checks to easily return home.
The findings published by Frontex on Tuesday have been seized upon by Brexit campaigners, including justice minister Dominic Raab who claimed the EU's free movement rules leave Britain "wide open" to crime and terrorism.
The report also 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 associated with the estimated one million individuals who reached the EU last year, but suggests many crossed two sections of the external borders of the EU.
The report 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."
EU citizens who had joined Islamic State in Syria are also taking advantage of the irregular migration flows to return home, the report found.
It 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 is evidence that the UK is at risk from terrorists able to slip through European borders, Brexit campaigners said.
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."
Vote Leave supporter Dominic Raab added: "This is a damning indictment by the very EU body charged with managing Europe's external border.
"Frontex has set out all too starkly the risks, including from crime and terrorism, that the EU's free movement rules leave Britain wide open to.
"With no solution in sight, the safer option is for Britain to leave the EU in order to regain control over our borders and immigration policy."
A spokesman for Britain Stronger in Europe insisted Britain has control of its borders.
"Britain has full control over our borders because we are not part of the EU's Schengen area," he said.
"Britain's deal with the EU gives us the best of both worlds - opting into things that help keep us safe, like co-operation on security issues, but opting out of things that do not work for us, like the borderless Schengen area."
Greek authorities this week warned that the EU-Turkey agreement to return migrants in Greece is threatened by a shortage of personnel to carry out assessments.
The Prime Minister has offered to provide more help to Greece as it struggles to implement the new deal.
David Cameron told his Greek counterpart Alexis Tsipras on Tuesday that additional support will be available in the coming weeks.