Brussels (AFP) - The European Union will "start falling apart" if it fails to take concrete action to tackle the migrant crisis within the next few weeks, Slovenian Prime Minister Miro Cerar warned Sunday.

"If we do not deliver some immediate and concrete actions on the ground in the next few days and weeks I believe the EU and Europe as a whole will start falling apart," said Cerar, whose tiny country of two million has been swamped by more than 60,000 migrants in a matter of days.

Cerar, who spoke as he went into an emergency summit on the migrant influx, said his country was facing a "very serious" situation and could not cope on its own for much longer.

The numbers arriving in Slovenia were proportionate to half a million arriving in Germany in one day, he said.

"We will not be able to endure this for weeks if we do not get help," the prime minister said, calling on neighbour Croatia not to continue pushing migrants onward to Slovenia on their way to other countries in the EU.

An unprecedented 670,000 people, mainly fleeing conflict in Syria, Iraq and Afghanistan, have flooded into Europe so far this year in the continent's worst crisis of its kind since World War II.

The majority cross from Turkey into Greece and then on through the Balkans with the aim mostly of getting to Germany.

Faced with a huge influx over the summer, Hungary clamped down on its border with Serbia, prompting the refugees to switch into Croatia which in turn imposed border controls, pushing them into Slovenia.

Germany and Austria have also introduced border controls after earlier opening their arms to the wave of arrivals, which has put Europe's cherished system of borderless travel in jeopardy.

Bulgaria, Romania and Serbia on Saturday warned they would not accept being turned into a "buffer zone" for the tens of thousands of arrivals streaming into Europe and would close their borders if Austria and Germany did so.

Sunday's mini summit, called by European Commission President Jean-Claude Juncker, groups the heads of 10 EU nations, including German Chancellor Angela Merkel, plus the leaders of non-EU Albania, Serbia and Macedonia.