More than 4,000 people walked across the border with Serbia just as the authorities in Hungary were completing preparations to seal the frontier.
Europe is struggling to cope with an enormous influx of people, mostly from Syria, fleeing violence and poverty.
Hungary has been criticised for how it deals with those crossing its border.
Officials estimate that 175,000 migrants have crossed from Serbia into Hungary so far this year.
Hungarian Prime Minister Viktor Orban has promised to seal the country’s borders and arrest any illegal migrants. The country is close to finishing a 4m-high (13ft) fence along the border with Serbia.
More than 4,000 Hungarian soldiers have been brought in to help police enforce a ban which Mr Orban has ordered must come into effect on Tuesday.
The BBC’s Nick Thorpe – reporting from Szeged near the Hungarian-Serbian border – says the humanitarian infrastructure to deal with the migrants is finally being established at the Roske migrant camp.
On Friday, footage emerged of migrants being thrown bags of food at the camp amid criticism that they were being treated like animals.
On Saturday, Austrian Chancellor Werner Faymann drew parallels between Hungary’s treatment of refugees and Nazi Germany’s treatment of Jews.
In response, Hungarian Foreign Minister Peter Szijjarto said Mr Faymann’s comments were “slanderous”.