A man at the property on Moncrieff Ave, Manurewa, last Tuesday morning said he was looking after the house for his immediate family who had allegedly left Auckland after making the find.
Vaaelua has also said the children were between five and 10 years old and had relatives living in New Zealand.
Police were also making "very good progress with DNA inquiries", Vaaelua said.
He confirmed the bodies of the children had likely been stored in the Papatoetoe Safe Store storage facility for three to four years before being discovered.
"Early indications suggest these children may have been deceased for a number of years before being found last week."
He was, however, hesitant to reveal too many details about what police knew of the renters or owners of the storage unit over concerns it may compromise the investigation.
When asked if police knew the identity of the people who were renting the storage unit, Vaaelua said: "Yes, we are following positive lines of inquiry in regards to the storage unit with the assistance of the storage company."
According to police, people living at the Moncrieff Ave house brought "unowned property to their address" on August 11.
"We reiterate that the occupants of the Moncrieff Ave property are not connected to their deaths," Vaaelua said last Thursday.
"They are understandably distressed by the discovery, and they have asked for privacy. We are ensuring there is support in place for them."
A neighbour earlier told the Herald there was "kids stuff in the back of the trailer", which transported the suitcases, such as prams, toys and a walker.
"We want to reassure the community our investigation is continuing to establish the facts to ascertain the full circumstances around the deaths of these children," Vaaelua said.
"This includes establishing when, where, and how. The nature of this discovery provides some complexities to the investigation."
