“It is expected that if he would come to Sweden this order would be carried out immediately,“ said prosecutor Lars Hedvall to news agency TT.
Sylvere Ahorugeze was arrested in 2008 while visiting Sweden when his wife was renewing her passport at the Rwandan embassy.
According to Rwanda, Ahorugeze, a Hutu, is under suspicion for taking part in the genocide against the Tutsi minority in 1994.
Among other things he is suspected of being responsible for the murder of one specific family and their neighbours, 28 people in total.
He denies all allegations and claims that the accusations are politically motivated, as the current Rwandan regime is dominated by Tutsis.
After being held in custody in Sweden for three years, Ahorugeze was released last summer after the Supreme Court (Högsta Domstolen) ruled that there was no reason to detain him while the decision from Europe was taking a long time.
Following his release, he returned to live with his family in Denmark, where he now resides.
However, in October last year, the European Court of Human Rights ruled that it was not wrong of Sweden to authorize the deportation.
The decision was then appealed to the highest authority, the Grand Chamber, which has decided not to review the case.
However, as Ahorugeze is living in Denmark, the Rwandan authorities will have to turn to the Danish - and not the Swedish - judicial system if they want Ahorugeze extradited, something the Danes so far have been unwilling to do.
“We can't have him extradited to us just so we can extradite him,” said Hedvall to TT.