Today, Katrina Casey, the ministry's head of sector enablement and support, said government officials were continuing to "stay in touch" with the school.
"Hornby High and the parent continue to meet to seek an outcome that will ensure the student's education continues and is not unnecessarily interrupted," she said.
"The school is continuing to encourage the student's return. He has on one occasion participated in an assessment of learning at school."
Earlier this week, Ms Parata refused to enter the debate.
"School rules and the enforcement of those rules are matters for school boards and school management," she said.
Boards of trustees are responsible for setting school rules on a wide range of matters, including those on uniform and appearance.
The ministry said facial hair was not grounds to stand down or suspend a student.
However, if a student repeatedly refuses to comply with school rules, that could amount to "continual disobedience".
"For this to result in a stand-down or suspension, the continual disobedience must be a harmful or dangerous example to other students at the school," the ministry says.
"In making any rules, such as those setting out a prohibition on facial hair, the board would be required to consider other laws such as those relating to human rights.
"For example there may be cases where exceptions are made in relation to facial hair to take into account a student's genuinely held religious beliefs."
