Austria's interior ministry said 6,500 people had crossed the frontier since Friday night when Hungary laid on buses after images of hundreds of desperate people walking along motorways made headlines worldwide.
A second group of at least 500 migrants began walking today from Budapest's main Keleti train station where there were ugly standoffs for days after authorities blocked migrants leaving the country by train.
But Hungary's police chief Karoly Papp warned this time there would be no help to reach Austria.
Hungary's hard line contrasted with a new more welcoming approach from some western European countries, with Finnish Prime Minister Juha Sipila offering to put refugee families up in his country home.
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"This has to be an eye opener how messed up the situation in Europe is now," Austrian Foreign Minister Sebastian Kurz said on arriving in Luxembourg for EU talks dominated by the crisis.
"I hope that this serves as a wake up call that (the situation) cannot continue."
At the Austrian border, people arriving off buses, exhausted but happy, walked across the frontier to the town of Nickelsdorf where authorities had set up a makeshift shelter.
"Austrians Danke schoen" ("Austrians thank you"), read a big sign waved by one refugee.
"My toes hurt, a lot of blood, we walked too much. I want to go (to) Germany, but then I stop," one 26-year-old Syrian man from Homs, who had both his feet wrapped in thick bandages, told AFP.
"We treated a two-day-old gunshot wound. We're seeing eye injuries caused by stun grenades. We're seeing bruising, including children with bruising," Red Cross spokesman Andreas Zenker told Austria's APA news agency.