The U.N. has estimated that more than a million migrants arrived in Europe via sea in 2015. Others have crossed into Europe overland from Turkey, which itself is estimated to be hosting around two million Syrian refugees. The U.N. also estimates more than 131,000 reached Europe through the Mediterranean so far this year. Southern European countries, Greece in particular, are struggling with the flow of people.
Many are fleeing civil war in Syria, although many are coming from impoverished countries in Africa and the Middle East and are seen as economic migrants rather than asylum seekers.
The flow of migrants has eaten away at European solidarity, creating deep tensions within the region and between countries. Austria, the Western Balkans and Eastern Europe, which are conduits for migrants heading to richer northern Europe, have refused migrants entry. Some have closed borders and opposed the EU's plans to resettle migrants throughout the bloc using a quota system.
Germany, meanwhile, has been fiercely criticized by other EU nations for opening its borders for a period, which some EU leaders said encouraged additional migration.
But so far, Germany is sticking with its acceptance of refugees.
"The humanitarian way is still the best one," Fuchs said. "Germany is a big country and we are a rich country."
—Holly Ellyatt contributed to this article.
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—By CNBC.Com's Leslie Shaffer; Follow her on Twitter @LeslieShaffer1