Syrians, Afghans and Iraqis accounted for more than half of the first-time applicants, Eurostat said.
Of those asylum seekers, 362,800 were from Syria -- double from 2014 -- while the number of Afghans quadrupled to 178,200 and Iraqis multiplied by seven to 121,500, according to the agency.
Germany had the highest number of applicants, with 441,800, or 35%, followed by Hungary with 174,400, Sweden with 156,100, then Austria, Italy and France.
The Eurostat figures come days before European Union and Turkish heads of state are due to meet to discuss the migrant crisis in Brussels, Belgium.
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'Crisis of European solidarity'
The U.N. refugee agency has issued recommendations aimed at helping resolve the crisis.
They include developing Europe-wide systems of responsibility for asylum seekers, including setting up a system for asylum requests "to be distributed in an equitable way across EU member states."
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"We are running out of time, and strong leadership and vision are urgently needed from European leaders to deal with what is, in our view, a situation that can still be managed if properly addressed," said Filippo Grandi, the U.N. high commissioner for refugees.
"This is as much a crisis of European solidarity as it is a refugee crisis."
'Imminent humanitarian crisis'
Europe is struggling to respond to the massive influx of migrants.
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Earlier this week, Grandi warned of an "imminent humanitarian crisis" in Europe as countries remained at odds over their response to the issue.
Austria and countries along the main Balkan migration route through Europe -- including Slovenia, Croatia, Serbia and Macedonia -- recently agreed to tighten border controls to slow arrivals to a trickle.
The move has created a rapidly growing bottleneck of migrants in Greece, a country facing severe financial hardships, as the flow of people there from Turkey continues unabated.
German Chancellor Angela Merkel said at a Berlin news conference Tuesday that the EU needed to stick to its obligation, made in September, to resettle 160,000 refugees among its members over two years. So far, few have been resettled.
Merkel also said European countries needed to reinstate the Schengen system of border-free travel within Europe to deal with the crisis. Many countries have implemented extra border controls in response to the migrant influx.
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Arrivals by sea
The International Organization for Migration estimates that 129,455 migrants crossed the Mediterranean Sea to Europe in the first nine weeks of this year. Some 418 people died trying to do so, the organization said.
The main nationalities have been Syrian, Afghan and Iraqi, it said.
"The numbers still fall far short of 2015's total, when over 1 million seaborne arrivals were recorded. But with 10 months left, it now appears likely that last year's total will be surpassed, possibly before the end of the summer," the organization said.
CNN's Lindsay Isaac and Tim Hume contributed to this report.
