As the conflicts in Syria and Afghanistan driving the movement intensify, the UN refugee agency predicted 700,000 people would reach Europe via the Mediterranean this year and "possibly even higher numbers" would come in 2016.
More than half of those who have made it to Europe have been Syrians fleeing their country's four-year civil war. Many have headed to Germany, which took in 280,000 migrants last month, more than in all of last year.
Some 200 Syrians and Afghans clashed in a mass brawl overnight in a Hamburg refugee centre, a former hardware store now sheltering 800 people, leaving four people injured, police said.
Fifty police were called in to contain the violence, which reportedly broke out after an argument in a shower block and saw two groups attack each other with iron bars, furniture and rocks.
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In earlier such disturbances, 14 people were injured Sunday when 70 Pakistanis clashed with 300 Albanians in a shelter in the central city of Kassel, before dozens of Syrians and Pakistanis came to blows Tuesday in a camp in the eastern city of Dresden.
Police union chief Rainer Wendt has proposed separating refugees by religion and nationality -- an idea quickly rejected by most lawmakers -- but today again warned that in some shelters "there are religious conflicts, inter-ethnic conflicts and criminals".