"Parents should be able to send their children to school confident that an individual of this type is not part of the school environment," Ms Parata said.
Manukau police have confirmed a 41-year-old man connected to the case was arrested on fraud charges on February 21.
He appeared in court on February 22 and was still in custody, a police spokeswoman confirmed.
Ms Parata said the person was facing charges in an Auckland court for breaching release conditions, but would not comment on whether further charges were expected.
She said schools involved in the case had been notified.
"School communities have been informed and the Ministry of Education is actively working with those schools. It is possible that several other schools have also been affected," she said.
"We have asked the courts to vary suppression orders so that we can work with other schools that may have been affected and they can inform parents."
Former Ombudsman Mel Smith will conduct the ministerial inquiry into the case and report back by the end of April.
The inquiry will look at how the offender was able to breach the system and how it can be strengthened, Ms Parata said.
"Clearly there are weaknesses in the system."
The person was registered as a teacher from 2000 and "working irregularly" in the sector since 2000, Ms Parata said.
"It is clear to us that this person has used multiple identities on multiple occasions."
The Teachers Council undertakes checks when teachers apply to be registered.
"A voluntary vetting is undertaken by police for that individual and with that individual's knowledge and consent," Ms Parata said.
"I have this morning called in the chair of the Teachers Council and the chief executive of the Teachers Council to ask them to give me an assurance of the integrity of the system they are responsible for."
She did not know whether the 2004 conviction was for an action that took place in a school, or while the offender was employed as a teacher.
Extended supervision orders are reserved for a person who has been convicted of a sexual offence against a person under 16 years old, and who have a real and ongoing risk of further sexual offences against minors.
These sexual offences include:
* specific sexual offences involving victims less than 16 years of age
* pornography offences involving persons under 16 years of age
* exploitative sexual offences against a person with a significant impairment.