The head of Germany's domestic intelligence agency says the deadly attacks in Paris and Brussels show the "highly complex" nature of the terrorism threat facing Europe.

Hans-Georg Maassen told a conference Monday that extremists returning from combat zones, home-grown extremists and extremists who have come in with Europe's recent wave of migrants were all involved in the recent attacks for which the Islamic State group has claimed responsibility.

Maassen says intelligence agencies now "need to take into account multiple attack scenarios by multiple cells against different targets and possibly over many days."

To help, he called for better cross-border information exchange. The German spy chief says "to counter criminal groups operating across borders, we need the enhanced international cooperation of security agencies."