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The court ruled that Peter Madsen, accused of the death of Swedish journalist Kim Wall, should continue to be detained.
“There are specific reasons to believe that were he released, he would make the prosecution of the case difficult,” it said.
On Tuesday, a judge ordered Madsen to be held in custody until October 3, a decision that he sought to overturn.
In a case that has gripped world audiences, Wall, 30, vanished after interviewing Madsen aboard his submarine on August 10.
Her headless torso was found floating in waters off Copenhagen on August 21.
Madsen maintained on Tuesday that she died when a 70-kilogramme (154-pound) hatch door fell on her head, and in a panic he threw her overboard. He insisted her body was intact at the time.
But prosecutors say he killed her and mutilated her body.
In a letter to the appeal court, Madsen’s lawyer, Betina Hald Engmark, argued there was no reason to suspect that he was guilty of “premeditated murder,” and said police had failed to present sufficient evidence about the alleged mutilation.
Madsen has been ordered to undergo a psychiatric assessment.
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