Germany has struggled to accommodate a wave of asylum-seekers from war zones such as Syria but also from countries without military conflict in southeastern Europe, including Albania, Serbia and Kosovo.
Europe's biggest economy has become the top destination for those fleeing war and persecution but de Maiziere said other European partners must also share the refugee load.
"The European Commission should act against member states that are not assuming their responsibilities," he told reporters as he announced the new official estimate.
Berlin had previously expected 500,000 asylum-seekers to arrive this year.
Chancellor Angela Merkel warned on Sunday that the asylum issue could become a bigger challenge for the European Union than the Greek debt crisis and urged a coordinated approach from Brussels.
Vice Chancellor Sigmar Gabriel, who described the jump in refugee figures as the "biggest political challenge of the coming year", had stronger words for the EU which he said has "failed miserably in this task".
A fair repartition of asylum-seekers was the "only sensible solution," he wrote on Facebook, calling it a "disgrace" that some EU member states were unwilling to pull their weight.
"We want free movement of people but, and I have said this often, the question is what does free movement of people mean in Europe.
"Therefore I aim to get a European answer on open borders," said the minister, who will meet his French counterpart Bernard Cazeneuve on Thursday to discuss the record influx of asylum-seekers in the EU.
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