The rescue operation was carried out off the coast of the Danish island of Saltholm near the Öresund Bridge.
An island resident told Danish network TV2 that two of the men had earlier knocked on the door of a house on Saltholm and appeared to be under the false impression that they had reached Sweden. They had apparently spoken poor English and said they wanted to seek asylum.
According to the witness they then asked the resident for a glass of water and left the home. The sea rescue operation got underway shortly thereafter.
A Copenhagen Police spokesman told TV2 that the group was rescued between Saltholm and the artificial island of Peberholm, where the water is around eight degrees.
“Four people were swimming around in the water. Three of them came onto land at Saltholm on their own and the fourth person was raised out of the water by a helicopter,” vice inspector Henrik Møller Jakobsen said.
By Tuesday afternoon, two of the four people were still in hospital receiving treatment, with one remaining on a respirator.
Jakobsen said that an investigation was underway, but did not release any information about the nationality of the four men. Police did say, however, that the men had most recently been living at a large asylum centre in Denmark.
“We are trying to figure out what happened. The first order of business is to determine if their papers are legitimate and how they got out there. Did they sail, were they brought out to Peberholm or did they get there some other way?,” Jakobsen said.
Despite Sweden recently tightening its residency rules, many migrants still perceive it as a more attractive destination than Denmark, where measures to reduce immigration have included passing a law that allows police to search asylum seekers for valuables.
Copenhagen police revealed last month that dozens of people have tried to walk over the high-speed Öresund Bridge that connects Copenhagen to Malmö in an effort to avoid Sweden’s new ID controls, which were implemented in January after it took in 163,000 asylum seekers last year and said it could not cope with the influx.
The crossing, made famous in the Nordic Noir detective series The Bridge (Broen), allows drivers to travel at up to 90 kilometres an hour and includes a motorway tunnel as well as an open air road section.
Copenhagen police have recently installed new warning signs designed to deter walkers as well as heat sensors to better allow them to trace people making the potentially deadly journey.
Ferry operators have also warned that growing numbers of asylum seekers are trying to get to Sweden from Denmark by clinging to the undersides of trucks boarding ferries in an apparent attempt to avoid the ID checks.