Detective Sergeant Derek Shaw said police interviewed and reinterviewed witnesses during the weekend and were conducting investigations into the circumstances surrounding the incident.
Reece Baydon Berland-Skerrett (22) was helicoptered to Dunedin Hospital on Thursday evening after being stabbed in the chest with a knife in a wooded area on the outskirts of Alexandra.
He underwent surgery for lung and near-heart injuries, after which his condition improved from critical to serious.
Mr Berland-Skerrett was later transferred to an open ward, where yesterday his health was continuing to improve.
On Friday, an Alexandra man was arrested and charged with wounding Mr Berland-Skerrett with intent to cause grievous bodily harm.
Hunter Craig Cavanagh (39) was remanded in custody without plea until July 2 after appearing before a justice of the peace at the Alexandra District Court on Friday afternoon.
It is alleged Cavanagh stabbed Mr Berland-Skerrett during a confrontation in pines near Boundary Rd about 8.30pm on June 26.