Europe's migrant crisis will be resolved at the EU's exterior border and beyond, German Chancellor Angela Merkel and her Austrian counterpart said Thursday.

Merkel, speaking alongside Austrian Chancellor Werner Faymann, said Europe needed to move faster with hotspots in Greece where refugees and other migrants can be registered, then fairly distributed around Europe or sent directly back home if their case for asylum does not meet the criteria.

"On the topic of refugees, there will be no solution when it's about reduction, when it's about order, when it's about controls, or when it's about legalization on the German-Austrian border," she said. "This has to be on the exterior borders of the European Union."

Germany has seen more migrants this year than any other European nation, with some 758,000 registered as arriving through October, and is struggling to keep up with the flow. Almost all have entered through Austria, primarily after entering Europe through Greece and then working their way north through the Balkans.

Germany has new regulations to streamline the asylum process for those fleeing civil war like Syrians but will also send home more quickly those from the Balkans or elsewhere who are just looking for better jobs.

Speaking on Germany's ARD television, Faymann said refugees have to be checked more closely in the wake of the attacks in Paris, but borders must not be closed.

"That would be the end of Schengen and the European idea," he said, referring to the Schengen passport-free travel zone of 30 European nations.

The most important goals, he said, is to end the violence in Syria that is forcing so many people to flee, improving refugees' situations in Turkey and coming up with better registration measures in Greece.

"We cannot solve the problem at either the Austrian or the German borders," he said.

Later, speaking alongside Merkel, he rejected calls for "simple solutions" to the refugee crisis.

"There is no simple solution that is sustainable and honest," he said.