Denmark has suspended all rail links with Germany after police stopped hundreds of migrants at the border.
Danish police also closed a motorway between the two countries when some asylum seekers began walking north after being forced off a train.
They say their destination is Sweden.
As the EU struggles with a major migrant crisis, the European Commission has proposed that 120,000 additional asylum seekers should be shared out between members, using binding quotas.
Denmark's DSB rail operator said trains to and from Germany had been suspended for an indefinite period because of exceptional passport checks.
Promise of papers
Two trains carrying more than 200 migrants are being held in Rodby, a major port with ferry links to Germany. Danish police say many migrants are refusing to leave the trains because they do not want to be registered in Denmark.
Police also closed part of the E45 motorway - the main road link between Germany and Denmark - after about 300 migrants left another train and set off on foot towards Sweden near the border town of Padborg.
Sweden has become a top destination for refugees after it promised to issue residency papers to all Syrian asylum seekers.
Denmark's new centre-right government has promised to get tough on immigration. Since its election in June it has slashed benefits for new arrivals and restricted the right to residency.
About 3,000 migrants have entered the country since the weekend.
Prime Minister Lars Lokke-Rasmussen said Denmark was under pressure as asylum seekers arrive on their way to Sweden.
"This clearly shows that what we are facing right now is not only a refugee problem, it is also a migration problem," he said.
A surge of migrants fleeing conflict and hardship in Africa and the Middle East has pushed north through Europe over the past few weeks.
Many of those escaping the civil war in Syria have travelled from Turkey across the sea to Greece, through Macedonia and Serbia, and then to Hungary from where they aim to reach northern Europe.
On Wednesday European Commission President Jean-Claude Juncker announced plans for a "swift, determined and comprehensive" response through a quota system.
In a "state of the union" annual address, he said tackling the crisis was "a matter of humanity and human dignity".
Among Mr Juncker's proposals:
- EU member states to accept their share of an additional 120,000 refugees, building upon proposed quotas to relocate 40,000 refugees which were set out in May (though governments then only actually agreed to take 32,000)
- A permanent relocation system to "deal with crisis situations more swiftly in the future"
- Commission to propose list of "safe countries" to which migrants would generally have to return
- Efforts to strengthen the EU's common asylum system
- A review of the so-called Dublin system, which states that people must claim asylum in the state where they first enter the EU
- Better management of external borders and better legal channels for migration
"It's 160,000 refugees in total that Europeans have to take into their arms and I really hope that this time everyone will be on board," Mr Juncker told the European Parliament.
The new plans would relocate 60% of those now in Italy, Greece and Hungary to Germany, France and Spain.
The numbers allocated to each country would depend on GDP, population, unemployment rate and asylum applications already processed.
Countries refusing to take in migrants could face financial penalties.
Next steps for EU leaders:
14 Sept: Special meeting of EU interior ministers on refugee crisis, with Juncker proposals on agenda
15-16 Oct: EU leaders' summit, with refugee crisis high on agenda. European Parliament then to decide on any new asylum measures with EU governments
Early 2016: EU proposals for better management of legal migration to EU due
Spain on Wednesday said it would accept a quota of almost 15,000 extra migrants migrants set by the EU.
However, Mr Juncker's proposals was criticised by both the Czech Republic and Slovakia.
Czech Prime Minister Bohuslav Sobotka said compulsory quotas were "not a good solution", while his Slovak counterpart called them "irrational".
France welcomed the first of 1,000 migrants it has pledged to take from Germany, having committed to receive 24,000 migrants over two years.
Germany has welcomed Syrian migrants, waiving EU rules and saying it expects to deal with 800,000 asylum seekers this year alone - though not all will qualify as refugees and some will be sent back.
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.