In an interview with Die Welt newspaper, Antonio Guterres called for more solidarity among European countries in taking in those fleeing war and persecution.
The responsibility must be "shared on many shoulders", said the UN High Commissioner for Refugees.
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"It is unsustainable in the long run that only two EU countries -- Germany and Sweden -- take in the majority of refugees," he added.
"All countries in Europe have the moral responsibility to welcome them and the clear legal obligation to protect them," said Guterres.
Germany, as Europe's top economy, has become the refugees' top destination.
One in three who arrived last year in the EU sought asylum in Germany.
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Berlin had predicted the number of refugees to reach 500,000 this year, but the Handelsblatt newspaper on Tuesday quoted government sources saying this figure could rise to 750,000.
New official figures are due to be published on Wednesday, and if that projection is confirmed, it would be a record and far more than the previous high in 1992, when Germany opened its doors to refugees fleeing the Balkans wars.
The sharp jump in numbers has left Germany scrambling to find ways to host the refugees, with tents and schools used as temporary housing.
State authorities have been calling for greater federal aid to cope with the demand.
German Chancellor Angela Merkel warned Sunday that the asylum crisis risks snowballing into a bigger challenge for Europe than Greece's debt woes.
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Development Minister Gerd Mueller called for urgent action from the EU, saying "the European Commission must switch immediately from vacation to emergency mode.
"We need an European Refugees Commissioner," Mueller told Tuesday's Passauer Neue Presse newspaper.
In the EU, Sweden recorded the next biggest number of asylum applications in 2014 -- 13 per cent, although as a proportion in relation to its population size, the country is shouldering the biggest burden in the bloc.
A record 60 million people around the world fled war, violence and persecution last year, according to UN data.
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