Dozens of parents have since complained about his conduct to the Catholic Primary School and to the Teaching Council of Aotearoa New Zealand.
Chief executive Lesley Hoskin, confirmed that the Council were considering complaints about the teacher's conduct.
"We aren't able to comment further on this as we are at the early stages of considering the information we have received," she said.
Hoskin emphasised that teachers, as members of society, we allowed to hold personal beliefs and opinions and engage in civil discourse.
"However, as they hold important roles in shaping children and young people's world views, it is important they manage their own assumptions and personal beliefs while teaching.
"Children and young people should be encouraged into learning critical thinking skills and making their own judgements about political, religious and societal issues."
All teachers were committed to upholding the Code of Professional Responsibility and Standards for the Teaching Profession, crafted specifically for the profession, she said.
"These set out the high standards for ethical behaviour that is expected of every teacher. All our investigations into allegations or concerns are informed by the Code and Standards and we look into whether a teacher has breached them."
Anyone with concerns about a teacher's conduct should first raise the issue with the school, "to give them a chance to investigate and clear things up," she said.
But if someone was unhappy with how the issue had been dealt with, they could escalate it to the NZTC.
The Herald understands the man's school, Manukau Christian School in Manurewa, has received threats following the incident. Police have not confirmed to the Herald whether threats were received.
The teacher's Facebook profile has been bombarded with angry comments and members of the public have written letters to the school demanding the teacher be disciplined or fired.
The Herald has attempted to contact the school and the teacher for comment. Principal Pete Slaney has reportedly said the incident is being handled internally and that the school does not condone racism.
On Wednesday the teacher apologised for the message that his actions had sent - which he said was unintended.
He said he understood that to "some people" the hat was a symbol of white supremacy but said that was not what it meant to him.
"I understand that to some people the hat represented a symbol of white supremacy and my wearing of it provoked them in unhelpful ways," he wrote.
"I am sorry that this is the communication that was received by many, and I am sorry for the hurt it caused. I would reiterate strongly that this is not the message I was trying to communicate."
He pointed to prominent celebrities including Kanye West and Candace Owens who also wear MAGA hats. He said he rejected "every form of racism and ethnic superiority".
"Be that as it may, I understand that the intended communication and the actual communication were two different things. As a result significant hurt was caused. For this I am deeply sorry. I would humbly ask that you find it in your hearts to forgive me."
