Migrants enter a bus, which is supposed to leave to Austria and Germany, at the Keleti trainstation in Budapest, Hungary, September 4, 2015. [Photo/Agencies]

Hungary cited traffic safety for its decision to move the migrants on. But it appeared to mark an admission that the government had lost control in the face of overwhelming numbers determined to reach the richer nations of northern and western Europe at the end of an often perilous journey from war and poverty in the Middle East, Africa and Asia.

On Friday, hundreds broke out of an overcrowded camp on Hungary's border with Serbia; others escaped from a stranded train, sprinting away from riot police down railway tracks, while still more took to the highway by foot led by a one-legged Syrian refugee and chanting "Germany, Germany!"

The scenes were emblematic of a crisis that has left Europe groping for answers, and for unity.

By nightfall, the Keleti railway terminus in Budapest, for days a campsite of migrants barred from taking trains west to Austria and Germany, was almost empty, as smiling families boarded a huge queue of buses that then snaked out of the capital.