Emergency services were called to Newtown Park Apartments which are owned by Wellington City Council just before midday on Tuesday.
A scene examination in Newtown will take place on Wednesday, after which there will be a blessing.
"The investigation continues to progress with the co-operation of the family, and police would like to assure the community there are no wider concerns for safety."
A post-mortem examination will be carried out.
Both Oranga Tamariki and Wellington City Council referred RNZ inquiries to police on Tuesday but said it would provide police with CCTV footage if requested.
In a statement, landlord Te Toi Mahana said: "Our thoughts are with the whānau and community during this very difficult time. Along with the Wellington City Council we are assisting the authorities with their enquiries."
Police said further updates would be provided when they were available.
