“Tracking those people and making sure they don’t take advantage of the Schengen framework will be an issue of special urgency over the next year”, he said, referring to the EU’s open-border zone.

Chertoff, who spoke at the Tatra summit, a conference in Bratislava, is part of a pressure group calling for more intelligence sharing between the US and EU states.

He noted that the US has a visa-waiver programme with most EU countries which could also be abused.

He said if the EU states wanted to protect the waiver it meant “we have to work closely together to identify people here who may come back from Syria and who might want to come to the US to carry out attacks”.

Chertoff’s warning echoed that of Julian King, the EU security commissioner, who recently told Die Welt, a German newspaper, that a surge in returning foreign fighters was “a threat we must be prepared to face” if IS lost territory in Iraq.

He said there were 2,500 European fighters in the Mosul area in Iraq alone.

Chertoff, as well as David Omand, a former director of the British intelligence unit, the GCHQ, said on Saturday that, foreign fighters aside, the threat of a cyberattack on EU or US targets was higher than in the past.

“You don’t have to bring people into a country to blow up something or to disrupt it, you can do it online,” Chertoff said.

He said IS did not need to have high-level IT experts to mount an attack because they could buy the cyber capabilities that they would need from organised crimes groups on the internet.

“If you have the money, you can buy the malware on the dark web and use it”, he said, referring to a hidden part of the internet.

Omand said it was also “inevitable” that there would one day be a terrorist attack using drones.

“We’ve already spotted Daesh doing that in Syria, so the idea is in people’s heads and it’s not so difficult to acquire drones”, he said.

He said the best way to stop such an incident was to rely on local police looking out for people “practicing or rehearsing that kind of attack”.

He added that he had not seen any sign that IS had acquired chemical or biological weapons from Syria’s arsenals.

“I’m retired, so I don’t have access to classified information any more … but I haven’t heard of such a development. I haven’t seen it. If they had those kinds of agents, they would have used them, or, at least, boasted about them”, he said.