More than 1,000 refugees are walking through Hungary to the Austrian border - and the Hungarian government says it is sending 100 buses to help them get there.
Hundreds fled from Bicske station - 35km from Budapest - while others broke out of the nearby camp set up to process their asylum claims.
Police clambered for their riot gear as the crowd made their break for freedom, but could only hold back a few.
One man collapsed and died during the commotion, according to Hungarian authorities.
The refugeeswere being held on the stationary train and ordered to register at the asylum centre in the town.
But several hundred who escaped are now trudging along the tracks towards what they hope will be freedom at the Austrian border 35km away.
They say women and children left behind at Bicske will follow on Saturday if the train is not allowed to continue.
The are refusing calls to register in Hungary and are adamant on making it to Germany.
Another long convoy of refugees has set out from a Budapest rail station after being told for days that no trains would be leaving for Germany.
A half-mile-long line blocked traffic at times as it snaked along a road in the Hungarian capital and onto a path beside a motorway.
They face a 171km trek to Austria.
The buses are now being organised to offer refugees transport to the Austrian border, according to the Hungarian prime minister's chief of staff.
Riot police used tear gas and batons on refugees during another camp break-out attempt on Friday - at Roszke, near the Serbian border.
About 300 refugees successfully fled the camp but police said they were able to round up the group after stopping motorway traffic.
Some 2,000 others held at the camp have threatened to leave unless their demands are met.
Elsewhere, footage showed refugees on the Greek island of Lesbos throwing stones at police and being dispersed by tear gas and stun grenades.
It is understood the refugees were attempting to board a ferry but were not properly registered.
The mayor of the island - which has about 15,000 refugees - said the situation was "a bomb about to explode" in his hands.
Earlier, a ferry sent by Greece had brought more than 2,000 rescued refugees from the island to Piraeus port, near Athens.
The deepening crisis comes as Hungary's PM Viktor Orban said the flow of refugees was "endless", adding: "We could end up a minority in our own continent."
The leaders of Hungary, Czech Republic, Poland and Slovakia have also rejected a quota system to share the refugees around the EU.
In a joint statement, they said a "mandatory and permanent quota for solidarity measures would be unacceptable."
Some 364,000 refugees have arrived in Europe so far this year, according to the International Organisation for Migration, with nearly 3,000 dying en route.
Prime Minister David Cameron has said Britain will take in "thousands more" refugees from camps on the Syrian border and provide an extra £100m in aid.
The apparent change of heart followed an online petition signed by more than 300,000 people.
The number of signatures jumped after pictures emerged of a three-year-old boy who washed up on a Turkish beach.
The boy, Aylan Kurdi, was buried on Friday in Kobani, Syria, alongside his mother and five-year-old brother Galip.
The boys' distraught father, Abduallah Kurdi, called on neighbouring countries to do more.
"I want Arab governments - not European countries - to see (what happened to) my children, and because of them to help people," he said.
Four Syrians have been remanded in custody in Turkey for arranging the family's sea crossing. They face charges of smuggling and involuntary manslaughter.
Austrian police have also revealed the 71 refugees found dead in a truck last week included Syrians, Iraqis and Afghans, but none had been identified.
Police chief Hans Peter Doskozil said they had likely died from suffocation shortly after entering the truck.
A number of people have been arrested, including the alleged driver.