He was scheduled to appear in the Auckland District Court on Wednesday before a judge to face the murder charge.
However, he remained in hospital and the court was unable to facilitate a video link to his bedside.
His lawyer sought and was granted interim name suppression before his next appearance, in the High Court at Auckland on March 20 at 9am. His name suppression will continue until at least that appearance.
Police were called to the Mt Albert complex about 1.15pm on Monday and found one person in a critical condition and the 25-year-old man with serious injuries.
Police spent days at the Kāinga Ora estate in Mt Albert, which consists of 20 one-bedroom units, and was known to have had security issues in the past. The agency spent almost $300,000 on private security for the complex, built in 2019.
Kāinga Ora earlier detailed the trouble caused by one of its residents at a complex where Rankin died, revealing it has been receiving complaints from neighbours for months.
Multiple people in the community told the Herald they were concerned one of the men they believed was involved in the homicide had been known to Kāinga Ora and police for at least a year before the incident.
“It could have been avoided,” neighbours say of the man’s death.