The convicted man has said he will not appeal, but prosecutor Göran Hansson has previously said he wants him to serve a life sentence.
The two victims were shot around twenty times with an automatic weapon in an apartment in the Hammarkullen area of Gothenburg.
Prosecutors are also appealing the acquittal of three men and a woman, who had been charged with being accessories to the murder and sheltering a criminal. Hansson will also appeal the six-month sentence passed down on a 48-year-old man convicted of sheltering a criminal.
Those convicted have until Friday to submit appeals.