Danish police said that about 70 of the refugees, who are understood to be mostly from Syria, arrived in Rödby in Denmark via two trains from Germany.
They were given food and drink at the station and were still waiting in the arrival hall when another train carrying around 100 more refugees arrived an hour later.
Some time after the second train pulled in, unrest spread through the station and a majority of the assembled refugees decided to flee through the surrounding fields.
Danish media reported that the group may have been scared that they could get sent back to Germany, rather than being allowed to move on to Sweden, where some of them are understood to have relatives.
Police said that many of the escaped refugees tried to head north towards Copenhagen on Sunday, which is connected to the southern Swedish city of Malmö by the Öresund bridge. But some of them were later tracked down by Danish officers.
"We have found the majority of them and they are in the process of getting registered so that there will be an overview," police spokesman Kim Kliver told TV 2.
“We will try again to explain to them that they have come to a safe and secure country, where we handle all of these kinds of asylum seekers properly,” he added.
Meanwhile authorities in Malmö said that around 70 refugees had turned up in southern Sweden on Sunday night and added that they were ready to welcome any others.
Nils Norling, a spokesperson for Swedish police in the region said that “no action” was required by officers, stating that the escaped refugees “have the right to apply to Migrationsverket (Sweden’s Migration Board) for asylum".
Fredrik Bengtsson, a spokesperson for Migrationsverket in Malmö told the TT news agency that extra staff had been called in and were working to find “around 300 accommodation places, should they be needed”.
“Shuttles between Germany and Denmark run all night and it’s not too far to Malmö,” he said.
“Most [refugees] who came to Germany the other day were told to stay there, but many of them have relatives in Sweden.”
Under the so-called Dublin rules, the first EU nation that an asylum seeker arrives in is supposed to process the claimant's application.
Denmark has a tougher approach towards migrants compared to its northern Nordic neighbour. Just over 9300 Syrians have moved to Denmark over the past year. Meanwhile Sweden has received asylum applications from more than 60,000 people.
Significant cuts in the welfare benefits afforded to asylum seekers were recently introduced in Denmark and the country has introduced one-year temporary residence permits for Syrian refugees and put made it harder for them to bring their family members to Denmark.