Hundreds of migrants have broken through police lines on Hungary's border with Serbia and are walking towards the capital, Budapest.
The migrants had earlier broken out of a registration camp at Roszke.
About 300 are on a motorway, escorted by police. Some later reportedly agreed to be bussed to a reception centre.
Meanwhile, the Greek government and UN refugee agency brought in extra staff and ships to deal with some 25,000 migrants on the island of Lesbos.
The processing centre has been set up on an abandoned football ground to help the stranded migrants.
The hope is that the centre - which will operate for five days - will help people to buy tickets for specially chartered ships to get to Athens, the BBC's Jonny Dymond on Lesbos reports.
Local authorities have been overwhelmed by the migrants who have been forced to live in squalid conditions, our correspondent adds.
Athens has already requested emergency EU assistance to deal with migrants arriving from Turkey.
Earlier, German Chancellor Angela Merkel warned that the "breathtaking" flow of migrants into Germany would change the country in the coming years.
Hungary has become a flashpoint as thousands of migrants and refugees from the Middle East and Africa move north to claim asylum in Germany and other countries.
The country's defence minister, Csaba Hende, resigned on Monday, reportedly over problems with the construction of a border fence meant to keep migrants out.
In other developments:
- The UK will accept up to 20,000 refugees from Syria over the next five years, David Cameron has told MPs
- At least 150 migrants in southern Denmark have tried to march towards the border with Sweden, forcing police to close a motorway
- The US administration "is actively considering a range of approaches to be more responsive to the global refugee crisis, including with regard to refugee resettlement", a White House spokesman has said
Hungary had previously blocked migrants heading north, insisting they be registered there first as required under EU rules. But it dropped restrictions on Friday after struggling to cope with thousands camping in Budapest.
About 20,000 migrants made their way from Hungary into Austria and Germany over the weekend.
At Roszke, scuffles erupted as some migrants who had broken out of a holding centre tried to force their way past police. Stones were thrown at officers, who responded with pepper spray.
About 300 managed to run to a nearby motorway, chanting "Germany, Germany". As darkness fell, they were walking, escorted by police, towards Budapest, 170km (105 miles) away.
Tensions building for days: The BBC's Nick Thorpe in Hungary
While Hungary has allocated $73m (£47m) to spend on a 175km (110 mile) fence along the Serbian border, no resources were devoted to humanitarian infrastructure at the police assembly point in a cornfield near Roszke.
There are only four toilets, and police and aid workers struggled to feed and keep people warm as the temperatures plunged to 5C (41F).
A shortage of buses to take them to a new registration centre just 2km away, and a shortage of interpreters to explain what was going on, led to the breakout from the field and a new march up the M5 motorway towards Budapest on Monday evening.
An estimated 340,000 asylum seekers have arrived in Europe so far this year, most braving dangerous sea journeys from North Africa and Turkey.
Germany, where most migrants are headed and which expects 800,000 asylum requests this year, has said it wants other EU states to help shoulder the burden. But the crisis has divided the 28-nation bloc.
French President Francois Hollande said mandatory quotas were being drawn up to relocate 120,000 migrants across the EU, and that France would take 24,000.
Earlier, Mrs Merkel thanked volunteers who had welcomed those arriving over the weekend, saying they had "painted a picture of Germany which can make us proud of our country".
However, she said that although Germany was "a country willing to take people in", it was "time for the European Union to pull its weight".
Mrs Merkel is facing criticism at home over Germany's willingness to accept so many asylum seekers. The Bavarian Christian Social Union, a sister party to Mrs Merkel's Christian Democrats, accused her of sending a "wrong signal".
Hungary, along with the Czech Republic, Slovakia and Romania, has rejected the idea of official quotas. Prime Minister Viktor Orban said "as long as we can't defend Europe's outer borders, it is not worth talking about how many people we can take in".
The Hungarian parliament last week passed tough new legislation on illegal immigrants.
The BBC's Nick Thorpe in Hungary says Csaba Hende's surprise resignation has been seized on by opposition parties as proof that the government's tough anti-migrant policies have failed.
He oversaw army efforts to construct a razor-wire fence in just six weeks but it was rechristened a "wire barrier" in recognition of its limited success.
In addition to the razor-wire barrier, the army is also building a 4m-high (13ft) fence along the border that was supposed to have been finished last month but remains largely incomplete.
Meanwhile, the influx of migrants shows no signs of abating. More boatloads arrived in the Greek islands on Monday, adding to an already desperate situation in some areas.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.