The group was among around 300 refugees who landed Sunday in Rødby in southern Denmark, which has Scandinavia's busiest ferry crossing to Germany.
But scuffles broke out with police when some ran off to avoid having their fingerprints taken in fear they would be registered as seeking refuge in Denmark and unable to go on to Sweden, where many said they had family.
Police said up to 150 had begun walking towards Sweden, which refugees typically reach by taking the train across a bridge linking Copenhagen and the Swedish city of Malmö. The bridge is not open to pedestrians.
Laila Saied, an engineer from Syria, said she had travelled through Europe with her husband and two children for one month in the hope of reaching Sweden.
"I slept on the street, I was on the sea with my children," she told broadcaster TV 2 News.
Police had said they wanted to resolve the situation "through dialogue" and after hours of talks most of those marching finally agreed to board buses taking them to a police station.
Prime Minister Lars Løkke Rasmussen said at a press conference that around 400 refugees had entered Denmark over the past 24 hours and that none would be allowed to continue to Sweden.
"We cannot just ignore our obligations and send them to Sweden without its consent, because then we would be doing the same as many other countries, which is the reason the European asylum system is under massive pressure," he said.
Rasmussen said he had told German Chancellor Angela Merkel that Denmark was willing to accept 100 refugees from Germany "given the very special situation Germany and Europe is in."
While Sweden has become a top EU destination for refugees by issuing permanent residency to all Syrian asylum seekers, Denmark has sought to reduce the influx by issuing temporary residence permits, delaying family reunifications and slashing benefits for newly arrived immigrants.
On Monday, the Danish government ran adds in four Lebanese newspapers publicizing those cuts.