The majority of the prisoners involved in the Waikeria Prison uprising are members of the Mongols and Comancheros, Kelvin Davis says.
Speaking after the 16 men who had destroyed the 'top jail' facility and occupied the prison's rooftop surrendered, the Corrections Minister accused them of "reckless criminal acts".
"Five of the men are deportees from Australia, with three subject to returning offender orders because of their criminal convictions," he said in a statement.
"The arson, violence and destruction carried out by these men were reckless criminal acts that put themselves, other prisoners, Corrections staff and emergency services in danger."
Davis added Police would be responsible for any charges laid.
Prisoners began their riot over what they claim are inhumane conditions and a lack of access to basic necessities.
A report last year following a surprise visit from the Ombudsman found issues with clothing and bedding, ventilation and sanitation in cells, poor access to cleaning supplies, and the general size and state of the cells.
However Davis says there is "never an excuse for resorting to violence and destruction".
"There are many legitimate avenues for prisoners to raise concerns about their conditions, including through the independent Corrections Inspectorate and the Office of the Ombudsman," he says.
"These prisoners used none of those avenues and never raised any issues prior to this event.
"No one should glorify the actions of these prisoners. They damaged property worth hundreds of thousands of dollars and they put their own lives and the health and safety of staff and other prisoners at risk."
Davis has been criticised for his response to the riot with National leader Judith Collins calling for Davis to "front up and explain how this loss of control happened and what he's going to do to fix it".
"He was perfectly happy to crow about prisons in Opposition but now that he's in charge, he's nowhere to be seen," she said on Saturday.
National's Corrections spokesperson Simeon Brown also called for Davis to "show some leadership" and visit the prison to ensure responders are supported.
"An independent investigation must be undertaken into how this riot started and whether the response to it has been adequate."
Also calling for Davis' intervention were Maori Party co-leader Rawiri Waititi and advocacy group People Against Prisons Aotearoa, which urged him to step in and intervene to ensure the prisoners got food and water.
However Davis says the containment of the riot was best left to Corrections staff, and criticised those who commented on the issue.
"These men wanted political attention, and unfortunately those who waded into the issue in order to generate headlines only helped to embolden them, extend the duration of the event, and increase the risk to safety.
"I made the decision not to bow to the demands of these men nor make public comment that would have simply opened up political negotiation with them and achieved nothing to bring the event to a safe resolution."
