The man arrested on suspicion of the killings, Mehdi Nemmouche, 29, reentered the EU via Frankfurt after spending a year in Syria and was subject to a "covert security check" before he travelled via France to Belgium, de Maizière told journalists in Luxembourg.
"Germany sent notification to France without the subject [Nemmouche] knowing," he said in comments reported by Welt newspaper ahead of consultations with his EU counterparts. De Maizière also questioned whether direct action should be taken in such cases rather than relying on tip-offs between agencies.
"Is it not perhaps better to stop these people?" he said before two days of talks that among other issues will review EU steps to identify foreign fighters and returnees from overseas conflicts.
Participants in the Syrian civil war with EU citizenship are of particular concern. Authorities in Germany know of around 320 radicalized young men who have gone to train at terrorist camps in the war-torn Middle Eastern country, according to the minister.
The probable return of "battle hardened and determined" fighters with the intent to stage terrorist attacks demanded better coordination among EU governments and law enforcers, he stressed.
Nemmouche was arrested in Marseilles on Friday after his baggage was found to hold a Kalashnikov assault rifle, a revolver and ammunition for both weapons, as well as clothing matching that of the Brussels shooter.
An Israeli couple and a French woman died in the May 24th attack and a Belgian member of the museum staff was injured.
The suspect, who comes from Roubaix near the Belgian border and already served five different sentences in French jails, was described by French prosecutors as a radicalized Islamist. He now refuses to be extradited from France to Belgium, his lawyers said.