The ministry has said some families expressed disappointment, hurt and sadness that after 40 years of trauma, that they are "still having to battle for a broader acknowledgement of the loss of their loved ones".
Parnell resident Jo Malcolm, whose father-in-law Alan Stokes died in the tragedy, is one of those opposed to the proposed memorial.
Today she presented the Waitematā Local Board with a petition signed by close to 700 people before giving an impassioned presentation as to why it should be built elsewhere.
"We are deeply disappointed at yesterday's turn of events. We are equally disappointed it would appear the ministry considers it is able to dictate the terms of this process, notwithstanding that it is the board that has responsibility for making the decision on land owner approval," she said.
"During the period of consultation and following it, a huge amount of work by a large number of people has gone into addressing the issues surrounding the proposed location of the memorial, including by the board, ourselves and other interested parties.
"During that time - around two months ago - the board announced the decision on land owner approval would be made today. There has been significant media interest [and] the overwhelming feedback from Waitematā is that this is the wrong memorial in the wrong park."
She accused the ministry of acting arrogantly by announcing less than 24 hours before the meeting that it was delaying its application.
"This board should be infuriated that the ministry should consider that it should be able to treat the board with such blatant disregard," she said.
"We are certainly furious that the ministry should have treated all of the interested parties - including Erebus family members - with such blatant disregard."
The ministry has said it will arrange an alternative time for the matter to be considered next year.
- RNZ