Migrants have flooded in to Budapest's Police Keleti train station as police leave, but the train operator says that there will be no trains going to Western Europe.

The rail company says its stance was due to "railway transport" security reasons.

Police shut down the Keleti terminal to migrants on Tuesday, preventing those with valid tickets but no travel documents from boarding trains to Austria and Germany, many migrants' preferred destination.

There was no immediate explanation from police or other authorities about Thursday's decisions.

Hungarian Prime Minister Viktor Orban is meeting European Union leaders on Thursday in Brussels.