Austrian police say around 6,500 refugees have reached Austria after the Hungarian government's surprise move to provide scores of buses for them.
Some 2,200 of them are already on their way to Germany, Interior Minister Johanna Mikl-Leitner told reporters at a rail station in Vienna.
She said earlier on September 5 that police would not use force to halt the influx after Austria and Germany threw open their borders to the waves of migrants.
Austrian police said they were expecting 10,000 arrivals out of Hungary. In Germany, police forces said they were preparing for the arrival of between 5,000 and 7,000 people.
A German federal police spokesman said 1,600 already had arrived at Munich's central station.
The German government has announced that those coming from Syria can apply for asylum.
Hungary had been blocking migrants for several days from traveling by train to Austria and Germany, saying it was obliged to register them.
Buses began arriving late on September 4 at Budapest's Keleti train station, which has become a makeshift camp for thousands of migrants.
Buses were also sent to collect over 1,000 migrants -- many of them from Syria -- who had set off by foot on September 4 down the main highway to Vienna.
It comes as European Union states are struggling to agree on how to deal with an unprecedented surge in migrants.
German government spokesman Georg Streiter told The Associated Press that the acceptance of migrants on September 5 was "an attempt to help solve an emergency situation. But we continue to expect Hungary to meet its European obligations."
More than 140,000 migrants have been recorded entering Hungary so far this year through the EU's external border with Serbia, where Hungary is building a 3.5-meter-high wall in a bid to stop the influx.
The crisis was discussed on September 5 in a meeting ofEuropean Union foreign ministers in Luxembourg.
EU foreign-policy chief Federica Mogherini said they had agreed to strengthen cooperation in several areas, including fighting trafficking networks and addressing the root causes of the crisis, particularly the conflict in Syria and instability in Libya.
Mogherini said the crisis was “here to stay” and that states must work together to deal with it effectively.
Finnish PM 'Sets Example'
Meanwhile, Finland's Prime Minister Juha Sipila says he will offer his home to refugees as his government doubled its estimate for the number of asylum seekers in the country this year up to 30,000.
Sipila said on September 5 that his home in Kempele, northern Finland, was little used at the moment and would house asylum seekers from the start of next year.
Sipila told national broadcaster YLE that an EU plan to distribute 120,000 refugees arriving in Greece, Italy, and Hungary to countries around the European Union should be voluntary and hoped Finland could show an example.
Meanwhile in Poland, Prime Minister Ewa Kopacz reiterated on September 5 that accepting 2,000 migrants is enough, given Poland's capabilities.
In July, Poland agreed to accept 2,000 migrants from Syria and North Africa by 2017.
Poland along with the Czech Republic, Hungary, and Slovakia has rejected any EU quotas for resettling refugees.