The latest tensions come as European leaders had mixed reactions to the European Commission’s call to share asylum seekers between the members, using binding quotas.
Two trains carrying more than 200 people have been stopped at the Danish port of Rodby, a major port with ferry links to Germany.
Danish police say the passengers have refused to leave the trains because they do not want to be registered in Denmark.
They say their destination is Sweden, a top destination for refugees after it promised to issue residency papers to all Syrian asylum seekers.
The train operator says police asked it to cancel the rail services to and from Germany as several hundred other migrants marched on a motorway towards Sweden.
Those on the trains refused to register with Danish authorities, which would mean having to apply for asylum in Denmark or returning to Germany.
In contrast to Sweden, Denmark has tried to reduce the influx of people by issuing temporary-residence permits, delaying family reunifications and cutting benefits for new arrivals.
The stand-off comes after the European Commission proposed an ambitious deal to share the burden of the humanitarian crisis, using binding quotas.
Commission president Jean-Claude Juncker was heckled as he reminded European leaders most of the continent is made up of refugees and migrants.
(Juncker:) “We should remember well that Europe is a continent where nearly everyone has, at one time, been a refugee.”
(Juncker:) “Our common history is marked by millions of Europeans fleeing from religious or political persecution, from war, from dictatorship, from oppression. Huguenots fleeing from France in the 17th century, Jews, Sinti, Roma, many others fleeing from Germany during the Nazi era of the ’30s and the ’40s of the last century.”
Under the plan to take in 160,000 additional people, Germany would take at least 31,000, France 24,000 and Spain almost 15,000.
Countries which refuse would be hit with financial penalities.
Germany’s Chancellor Angela Merkel has urged the bloc to go even further than Mr Juncker’s proposal.
Ms Merkel has called for a distribution of migrants with no limits on actual numbers.
“We need a binding agreement on a binding distribution of refugees among all member states, according to fair criteria. It can’t stay the way it is right now. But it would be a step forward if we could achieve what Jean-Claude Juncker is proposing.”
However, the leader of Britain’s Eurosceptic UKIP party, Nigel Farage, has told the European Parliament the European Union is mad to take so many.
Mr Farage says he believes most of the people arriving in Europe are economic migrants.
He has urged the British parliament to look to Australia for inspiration on the issue.
“We must be mad to take this risk with the cohesion of our societies. If we want to help genuine refugees, if we want to protect our societies, if we want to stop the criminal trafficking gangs from benefiting as they are, we must stop the boats coming, as the Australians did. And then we can assess who qualifies for refugee status.”
In Australia, Prime Minister Tony Abbott has announced plans to accept an extra 12-thousand people fleeing from Syria and Iraq.
It came as he confirmed Australia would bomb targets of the self-proclaimed Islamic State in Syria.
In the United States, Secretary of State John Kerry says the Obama administration also aims to allow more refugees to resettle there, including a larger number of Syrians.
“We are committed to increasing the number of refugees that we take, and we are looking hard at the number that we can specifically manage with respect to the crisis in Syria and Europe and their migration today.”
Meanwhile, at least 400 people have broken through police lines at the flashpoint town of Roszke on Hungary’s southern border with Serbia.
They yelled “No camp!” as they scattered in all directions.