He said police had been speaking with the family, and there was a lot they were not being told because he had some "very obvious injuries and we simply don't know how that happened".
Foster said on Friday the investigation was "still going well but will remain a lengthy investigation due to medical reports from experts" and others.
The house was initially treated as a crime scene, but Foster said the initial examinations were completed in the first few days following the incident.
The boy was found at the address on January 29 by a family member and was subsequently taken to Hawke's Bay Hospital by ambulance.
Two days later he was transported to Starship Hospital in Auckland where he remains in a stable condition.