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.
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.
Hungary had previously blocked those 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.
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.
Images of migrants crossing the barrier mocked Prime Minister Viktor Orban's determination to keep them out of Hungary, our correspondent adds.
