Some of them have tried to rectify the unwanted situation by requesting the removal of one of the foetuses in Norway, which allows for foetal reduction. All of the requests, however, have thus far been denied.
But Danish women aren't the only ones seeking the treatment in Norway.
“So far we have received eight requests for foetal reduction from foreign women. All have been rejected,” Torbjørn Eggebø, the chief physician at the foetal medicine department at Trondheim's St. Olav's Hospital, told Vårt Land.
The women came from Denmark Sweden, Italy, Germany and Ireland and were turned away because they could not prove that they reside in Norway. Eggebø said.
The requests came after Norway's health authorities ruled that foreign women pregnant with twins should be allowed to abort one fetus in Norwegian hospitals, even if it is perfectly healthy.
The ruling was expected to open the way for women from neighbouring Sweden and Denmark, where the procedure of “selective reduction” is not permitted in the same way.
“All women, regardless of whether they are Norwegian or foreign women residing in Norway have the same right to abortion and fetal reduction,” Torunn Janbu from Norway's Directorate of Health told NRK in October.
While St. Olav's Hospital has denied requests because women cannot prove they reside in Norway, hospitals are not required by law to ask for a fixed address. This has led to concerns that Norway could face a new form of abortion tourism.
Foreign women are looking to Norway due to an interpretation of the nation's abortion law by the Justice Ministry's legal department. Although the law does not mention foetal reduction specifically, the ministry's interpretation ruled that there is no legal obstacle to stop women who are pregnant with twins or more from aborting one or more of the healthy foetuses.
Torunn Janbu from Norway's Directorate of Health told The Local Norway in October that the body "[doesn't] have anything to say about the ethics" of the procedure.
“We just inform the local health services about how to apply the law," Janbu said.
When Norway's abortion law was introduced in 1975, foetal reduction was not a medical option as it is now.
Just before Christmas, the Norwegian parliament rejected a proposal from the Christian Democrats and the Centre Party that would have made foetal reduction illegally.
In Denmark, pregnant women are allowed to reduce the number of foetuses to two, but not to one unless there are health risks.