On the possible closure, Ms Parata said there was "a process that we have to step through".
"It has always been one of the elements of the model, that in the event that a school fails, that it can be shut down.
"But that has to happen in accordance with the actual legal agreement that we have with the school, so we have to work through that process. I'm not ruling it in, or out."
One potential problem for the Government is whether it can recoup some of the $1.6 million implementation and establishment fee given to the school.
The ministry said a verified roll would not be known until next month.
A series of articles in the Herald have exposed ongoing problems at the school and the fact it was opened against advice from the ministry.
School 'unable' to accommodate 65 students
Children are being taught in temporary classrooms after a new charter school faced consenting issues and struggled with the short turnaround time after being selected.
Te Kapehu Whetu (Teina) did not have all facilities in place in time for its February 16 opening, the Ministry of Education said.
"Due to the short establishment timeframe and delays in the consenting process, [the school] was not able to have all of its facilities in place in time for opening, so they were unable to accommodate 65 students," the ministry's head of sector enablement and support Katrina Casey said.
"There is no concern in this regard. It is not unusual for new state schools to start with a roll that is below the level funded for the first three years."
The Whangarei primary school is run by the He Puna Marama Charitable Trust, which for over a year has run the successful charter school, Te Kura Hourua O Whangarei Terenga Paraoa.
Trust chief executive Raewyn Tipene said that, although there had been consenting issues for the new school, it was always planned for some facilities to be completed after opening.
The pre-fab classrooms currently being used are in very good condition, she said.
All 40 students who were eligible started Term 1, Ms Tipene said, and there are 20 on a waiting list, who will start over the year as they turn 5.
"There isn't a facility 'situation'. All eligible students have started. In fact, we have more than we planned."