Kim Hjelmgaard

USA TODAY

DAVOS, Switzerland — European leaders warned Thursday that the continent's refugee crisis is growing, and if it's not brought under control by spring, it could push the region past the breaking point.

"We see today that in the first three weeks of the year, there were 35,000 people crossing the (Aegean Sea to Greece) from Turkey," Mark Rutte, Holland's prime minister, said. "Last year, it was only 1,600 in the full month of January. When spring comes, the numbers will quadruple. We can't cope with these numbers any longer."

Millions of migrants from the Middle East have made their way through Turkey en route to northern Europe.

Rutte said the European Union has six to eight weeks to get a grip on the crisis, echoing similar remarks made this week by European Council President Donald Tusk.

"When spring comes, the number of refugees coming out of Turkey and Lebanon and other countries through Greece and the Western Balkans and into the rest of European Union (will rise)," Rutte said.

He spoke at a panel discussion on Europe's future during the World Economic Forum's annual meeting.

Reporter's notebook: Walking with migrants

Rutte said the immediate priority for policymakers is to make a success of an EU plan with Turkey to limit the number of people trying to reach Europe from its territory. He said it was necessary to ensure that measures to more equitably redistribute asylum seekers across the 28-nation EU were working. The EU has admitted they are not.

Alexis Tsipras, Greece's prime minister, was on the same panel. "What is happening in the Aegean is a great shame for our common European culture and civilization. On a daily basis we are faced with a death toll in the sea because (people) traffickers are working there unimpeded," he said.

German Finance Minister Wolfgang Schäuble said the entire European political leadership agreed the influx was too high, but it would be a "disgrace if Europe were turned into a fortress."

Nearly 4,000 people drowned trying to reach Europe in 2015, the United Nations' refugee agency estimated. This year, 95 people have died crossing the Mediterranean Sea, according to the International Organization for Migration.

IMF says Europe's refugee crisis to boost region's GDP

After a separate presentation on the subject by the Swedish delegation, Prime Minister Stefan Löfven told USA TODAY he was not "naive enough to think that" getting all 28 EU member states to live up to their responsibilities over the crisis "was going to be easy." Löfven was flanked by Morgan Johansson, his migration minister, who said Sweden had not discussed the idea of putting a "ceiling" on the number of asylum seekers it accepts.

"What do you do when you reach that ceiling? We are bound by the Geneva Convention on our duty to accept refugees," he said.

Sweden has taken in 160,000 refugees, double the amount it allowed in during the Balkan Wars in the 1990s. On a per capita basis, the country has absorbed more refugees than Germany, which has let in 1 million people fleeing conflict zones from Afghanistan to Eritrea to Syria.

In the past four months, Johannson said, 26,000 unaccompanied minors have crossed into Swedish territory.

Löfven, Sweden's leader, downplayed a recent spat with Denmark after the two nations accused each other of exacerbating the crisis by imposing border controls.

"I have a very good relationship with the Danish prime minister," Löfven said. "We phone one another and send text messages."

Cameron says migrants must learn English