The head of the EU police agency, Europol, says there are no guarantees that another Paris-style terror attack can be prevented despite increased security measures.
Rob Wainwright said that it has become "extremely difficult" to deal with the threat posed by Islamist extremists.
It comes as British Prime Minister David Cameron vowed to tackle what he called the "poisonous narrative of Islamist extremism that is turning too many young minds".
He was speaking following two days of talks with US President Barack Obama in Washington, where they said a new group would be set up to exchange information and expertise to tackle the terror threat.
The two leaders also agreed to stage cyber "war games" and establish a joint "cyber cell" to boost both countries' resistance to hack attacks.
There are fears about the spread of terrorism after last week's Paris attacks that left 17 people dead and the arrest of more than two dozen people in anti-terror raids in Belgium, Germany and France.
Mr Wainwright admitted that stopping every potential attack was "very difficult" but vowed to "prevail" and said there was a determined action by police to disrupt cells.
He said: "Even in countries like France that have some of the most well-equipped counter-terrorist capabilities in the world, still it is possible for terrorist attacks to take place."
"This means that stopping everything is very difficult. Containing the threat fully is very difficult but I'm sure we will prevail in the same way as societies have prevailed against other forms of terrorism in the past."
Mr Wainwright said the terror threat was "very serious" and a "large-scale problem" across many European countries and there could be thousands of suspects radicalised online and through their experiences in Syria and Iraq.
It comes as EU foreign ministers will meet in Brussels on Monday, to discuss the heightened threat of terrorism in Europe.