"We already need in the coming weeks a sustainable, tangible and clear reduction in the number of refugees coming to Europe and Germany," de Maizière told journalists after the meeting of EU interior ministers.
For de Maizière, the situation is serious enough to endanger the Schengen free movement zone and its economic benefits for all of Europe. Five nations have already reintroduced some form of border controls.
"If Schengen ends up in danger, then all Schengen member states are affected, economically, politically, and we don't want that."
Hardliners among the 26 Schengen countries are already pushing for the reintroduction of border controls for two years – a move allowed "in the case of exceptional circumstances" under the treaty governing the agreement.
But leaders including Chancellor Angela Merkel, who has nailed her colours to the mast of free movement, see that option as an acknowledgement of failure as well as a potential economic millstone.
As well as putting pressure on Greece, the Chancellor has repeatedly asked Turkey to do more on its side to prevent people from making the crossing into Europe.
DON'T MISS: Merkel pushes Turkey to stem flow of migrants
'First part of the corridor'
Many refugees from the Middle East first set foot on European soil in Greece, where the sea crossing from Turkey is shortest.
Hundreds of thousands have arrived in recent months to take their first steps on the so-called "Balkan route" which leads through south-eastern Europe towards Austria, Germany or Sweden.
Efforts to set up reception centres in Greece and Italy, another main entry point into the Schengen zone, have so far stumbled, with Greece – still far from recovered from its economic crisis – saying it needs help from its EU neighbours to master the situation.
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"What do you want us to do?" Greek Interior Minister Ioannis Mouzalas asked. "Under international law, our only possibility for action is to save people [from the sea]."
"Greece is not the door, but the first part of the corridor to Europe," Mouzalas added.
While de Maizière acknowledged that there was more the rest of Europe could do to support Greece, including boosting resources to the border agency Frontex, Austria was less forgiving.
"If we do not manage to secure the European external border – i.e., the Turkish-Greek border – then the external border of Schengen will move towards Central Europe," Austrian Interior Minister Johanna Mikl-Leitner said – apparently mooting expelling Greece from the free-movement zone.