On Tuesday, Children's Minister Kelvin Davis revealed Oranga Tamariki had been involved with the young boy's family.
The extent to which the ministry had involvement with Malachi and his care arrangements is still unclear but, in a statement, its acting chief executive Chappie Te Kani said he is "committed to understanding where [Oranga Tamariki] may have failed Malachi and his whānau".
He says chief social worker Peter Whitcombe will undertake a practice review alongside an independent reviewer.
"The chief social worker's investigation will look at what we knew, how we responded and whether the decisions made based on the information was appropriate. It will also consider whether our current assessment procedures and processes need to be modified.
"If Oranga Tamariki failed Malachi, or if we have fallen short to provide him care and protection, I will own it and we will change."
In an earlier statement this week, Te Kani said he was in the process of establishing exactly what involvement the ministry had with Malachi.
"We need to get to the bottom of why this happened, whether there was more we could have done, and what we can do to ensure such an awful tragedy never happens again."
He says the agency will meet with Subecz's whānau in the coming days but understands no improvement to the agency will fill the hole left behind by his death.
"I don't think anything I or Oranga Tamariki does will be able to do that. But I do want to assure Malachi's whānau that, regardless of the outcome of this or any other reviews or investigations, Malachi will be a constant reminder of why Oranga Tamariki needs to do better and the entire children's system needs to be better.
"The price we pay for delivering anything less is too high a price for all of us."
