Germany reimposed border controls on Sunday after Europe's most powerful nation acknowledged it could scarcely cope with thousands of asylum-seekers arriving every day.

A day before deeply divided European Union ministers tackle the migrant crisis, the U.N. refugee agency also called on every member state to take in a share of asylum-seekers under a Brussels plan which some countries are fiercely resisting. 

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"The aim of these measures is to limit the current inflows to Germany and to return to orderly procedures when people enter the country," said German Interior Minister Thomas de Maiziere.

Open borders among the European countries which signed the Schengen Treaty are a crucial part of the EU project, but controls can be re-introduced, provided they are only temporary.

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"The free movement of people under Schengen is a unique symbol of European integration," the EU's executive Commission said in a statement. "However, the other side of the coin is a better joint management of our external borders and more solidarity in coping with the refugee crisis."

Germany has become a magnet for migrants making journeys by sea and land, often via Turkey and the Greek islands, and then onwards through the Balkans, Hungary and Austria. Police said around 13,000 arrived in the southern German city of Munich alone on Saturday, and another 3,000 on Sunday morning.