Conevski, serving a life sentence for the murder of two youths at Femøren on the island of Amager near Copenhagen in 1984, will not be released after the court on Monday rejected his application for release on parole.
Former taxi driver Conevski murdered two Danish youths who were camping at the Femøren area near the Amager beach on May 20th, 1984.
He ordered three friends out of the tent in which they had been sleeping before killing two, a 16-year-old and a 20-year-old, by shooting them in the head.
The third of the three young men, also aged 16 at the time, managed to escape despite being fired at.
Conevski was sentenced a year later to lifetime imprisonment following the cold-blooded crime, which left Denmark in shock.
He was also convicted of attempted murder and several other serious crimes.
After serving over three decades of his sentence, the now 68-year-old double murderer wanted to be released and sent to Macedonia, where his wife, children and grandchildren live, writes Ritzau.
This request was rejected by Copenhagen City Court in May, and Conevski's appeal was subsequently referred to the higher Østre Landsret court.
Following his conviction in 1985, Conevski was later diagnosed as insane and was transferred to Denmark's Sikringen special unit for dangerous mentally ill prisoners.
The decree declaring him dangerous was later lifted, and the 68-year-old is now detained at a secure wing of the St. Hans hospital in Roskilde.
Assessments by doctors at that unit find him to have been stable for an extended period, reports Ritzau.
Authorities have on several occasions assessed the viability of transferring him to Macedonia, according to the report.
These considerations have not proved enough to convince the court that Conevski can be released on parole.