On Maundy Thursday, the man, who is in his 25s, admitted that he killed the woman but that it was not his intention.
District Attorney Kristoffer, however, considers that he has sufficient reason to suspect that it is a case of murder.
A suspected murder weapon has been found while diving in a lake in Höör.
The technical investigations of the object continue, the police stated yesterday.
Initially, a preliminary investigation into suspected kidnapping was launched, but on Wednesday it turned into a preliminary investigation into murder.
The woman left a friend's home at two o'clock during the night until Tuesday. She never came home. After a large search operation, a body was found on Wednesday.