European Council President Donald Tusk has issued a stark warning that the European Union has "no more than two months" to tackle the refugee crisis engulfing the 28-nation bloc or else face the collapse of its passport-free Schengen zone.

Tusk was speaking to the European Parliament in Strasbourg on Tuesday amid growing frustration in Brussels and Germany - the bloc's biggest economy and main destination for migrants arriving in Europe - that the EU seems unable to resolve its worst migration crisis since World War II.

"We have no more than two months to get things under control," Tusk, who chairs the summits of EU leaders, said.

"The March European Council [summit] will be the last moment to see if our strategy works. If it doesn't, we will face grave consequences, such as the collapse of Schengen."

The European Council summit on March 17-18 will focus mainly on the refugee and migration crisis.

The Schengen system has already been suspended in some countries such as Denmark, Germany and Sweden, which have introduced controls at their borders in order to stem the flow of migrant and refugee arrivals.

Tusk said that EU governments had failed to deliver on commitments to curb the flow of refugees and migrants reaching Europe, with more than one million arrivals last year and figures showing little sign of decreasing over the winter months.

Greece reported 100,000 new arrivals in December alone and further north, thousands of refugees are caught in sub-zero temperatures as they attempt to cross the Balkans to countries like Germany.

REPORTER'S NOTEBOOK: Refugees look to the sea as Sweden tightens land border

"Unilateral actions from different European states and EU states to suddenly close borders have pushed people towards more dangerous routes in the hands of smugglers again," said Doctors Without Borders adviser Aurelie Ponthieu.

"That's something we're seeing today- more and more people resorting to smuggling routes and the services of smugglers to cross through the Balkans and stranding people behind borders without any assistance."

Tusk said on Tuesday that a landmark deal with Turkey, which is meant to keep more people on its soil in exchange for funding for refugees and reviving its long-stalled EU membership talks, "was still to bear fruit".

He said the EU would "fail as a political project" if it could not control its external borders properly.

The crisis has exposed bitter disputes among EU countries, with some blaming Greece and Italy for letting too many people in. Athens and Rome say Germany's initial open-door policy encouraged more arrivals than anyone could cope with.

More than 3,800 refugees died trying to get into Europe in 2015.