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 from Budapest's main Keleti train station on Saturday 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.
"The provision of buses towards Austria was a one-off and there will no be more vehicles sent to refugees walking along the road," he told a news conference, state news agency MTI reported.
Hungary's hard line contrasted with a new more welcoming approach from some western European countries led by Germany -- where most migrants want to go -- after an outpouring of sympathy for the refugees.
"This has to be an eye opener how messed up the situation in Europe is now," Austrian Foreign Minister Sebastian Kurz said as he arrived in Luxembourg for EU talks dominated by the crisis. "I hope that this serves as a wake up call that (the situation) cannot continue."
'Sliver of humanity'
Refugees waiting for buses in Nickelsdorf. Photo: Martin Pusch/ORF Report
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.
Red Cross medics were on hand at the border to tend to the sick and injured. "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.
Austrian police said they expected the number of arrivals to reach 10,000 people by the day's end.
"The streams (of people) keep coming," Hans Peter Doskozil, chief of police in Burgenland state, said.
Most boarded special buses and trains to Vienna, from where they planned to continue on to Munich, or other German cities, on the last leg of their perilous odyssey.
In Vienna, they were greeted by a small army of volunteers handing out food, drinks, sanitary products and train tickets.
"After endless examples of shameful treatment by governments of refugees and migrants in Europe, it is a relief to finally see a sliver of humanity," said Amnesty International's Gauri van Gulik, calling for "the pragmatic and humane approach" to become "the rule, not the exception."
Hungary is a key point of entry to the EU for migrants and refugees from the Middle East and Asia trekking up through the Balkans to western Europe after crossing the Mediterranean to Greece. A record 50,000 entered the country in August alone.
The right-wing government of Prime Minister Viktor Orban, which has built a razor-wire anti-immigrant fence all along the border with Serbia, has swung wildly in its approach to the crisis over the past week.
After barring migrants from leaving the country for days -- and trying to force them to register at refugee camps from which hundreds escaped Friday -- the government laid on 90 buses Friday to hasten their journey westwards.
Hungarian Foreign Minister Peter Szijjarto on Saturday blamed the "failed migration policy of the EU" for the refugee crisis, the worst in Europe since World War II.
New data from the UN refugee agency, UNHCR, on Saturday showed that 366,402 migrants had crossed the Mediterranean to Europe this year, with 2,800 dying or going missing en route. Forty-nine percent were escaping Syria's civil war and jihadist groups.
Split on quotas
The human cost of the Syrian exodus was made horrifically clear this week by photographs of the body of a three-year-old Syrian boy, Aylan Kurdi, washed up on a beach in Turkey.
Aylan, his brother and mother died after the boat in which they were crossing the Aegean Sea to Greece capsized.
On Saturday morning, migrants on the Greek island of Lesbos, where many migrants land, scuffled with police, angry at the delay in registering them for onward travel to Athens and the rest of Europe.
EU foreign ministers met in Luxembourg on Saturday to discuss the crisis. European Commission President Jean-Claude Juncker has proposed mandatory quotas for resettling 160,000 refugees across member states.
France and Germany -- which expects to receive 800,000 asylum applications this year -- back quotas but Hungary, the Czech Republic, Poland and Slovakia rejected any such imposition on Friday.
"We must not forget that those who are coming in have been brought up under a different religion and represent a profoundly different culture," Hungary's Viktor Orban wrote in a German newspaper this week.
"The majority are not Christians but Muslims. That is an important question because Europe and European culture have Christian roots."