She said it is appropriate to commemorate the victims of one of this country's most tragic events, which is likely to be located in Auckland.
"This will be well-received by many family members of the Erebus victims and acknowledges the departure location of the flight," Graham said.
Brodie Stubbs, the ministry's manager of memorials and taonga, said the memorial would not be ready in time for the disaster's 40th anniversary in November next year.
"What we learnt with our involvement in the Canterbury Earthquake memorial, particularly in relation to the involvement of family members, is that you can't do it too quickly.
"Our feeling is that trying to hit that symbolic target of the 40th anniversary would have been at the expense of good involvement and consultation with the families," he said, saying the process was almost as important at the final outcome.
Stubbs said the aim was to have the memorial completed in May 2020.
Graham said initially there was some frustration among the families the memorial would not be ready for the 40th anniversary, but they had got over the disappointment and now of the view it was better late than never.
The ministry is working with Auckland Council, iwi, local government and community groups to select an appropriate site, said Graham.
"The design brief includes ideas and information from those families and groups about what they would like the memorial to include," she said.