“Data protection is all well and good, but in times of crisis security comes first,” de Maizière told public broadcaster ARD.
“The external borders of the Schengen zone have too many gaps in them. We need a register which shows who's coming in and who's leaving.”
The minister also called for joining up the various “data pots” which security services in EU member states compile.
“Europe as a whole is threatened and we need common solutions to terrorism,” he argued.
The interior minister also said that he believed there was a link between the Brussels bombings and terror attacks in Paris last November, which left 130 people dead.
“The way in which the attacks took place suggest it was the same network, the explosives were probably also developed in a similar way.
The terror alert in Germany remains high, just as it was before the Belgian attacks, the interior minister added.
On Tuesday a series of bombings claimed by the Islamic State group ripped through Brussels airport and a metro train, killing around 35 people in the latest attack to bring carnage to the heart of Europe.
Two massive suicide blasts by attackers with bombs in their bags hit the check-in hall at Zaventem Airport, strewing the scene with blood and mangled bodies and sending hundreds of terrified travellers fleeing in terror.
German police and security services were placed on high alert, especially at airports and train stations and on the nation's western borders with Belgium, Luxembourg and the Netherlands.