A memorial for the 257 people who died when an Air New Zealand scenic flight to Antarctica crashed into Mount Erebus in 1979 was originally planned for Auckland's Parnell Rose Garden.
But flood damage last year forced families and the ministry to find a new site.
Ministry of Culture and Heritage secretary Laulu Mac Leauanae said potential sites continued to be discussed and put forward with stakeholders.
He said Pukeahu National War Memorial Park in Wellington and the area adjacent to the Sir Michael Joseph Savage Memorial in Ōrākei, Auckland, were being considered.
One Erebus family member had since spoken out against building a national memorial on the site of another.
"It's totally unsuitable. First, obviously because it's a war memorial, and this isn't about a war memorial.
"Secondly, just because of the location - it's in the middle of a pretty busy part of Wellington city, and it really doesn't tick any of the boxes that we identified as Erebus family members."
Stewart said a memorial was first announced in 2017.
"My own older brother, at the time, was interviewed and said, 'Well, look, none of us are getting any younger and we'd really like this to be resolved sooner rather than later.'
"Well, he's since passed away, so he will never be able to go to that memorial."
He said is past time to do something.
"I'm just fed up with hearing that. And we've just seen in the news recently that there's been a memorial in the Netherlands for the victims of the flight that was shot over Ukraine, only 10 years ago, and we've waited 45 years, so we really want them just to get on with it.
It was his understanding more families preferred a site in Auckland.
The Ministry for Culture and Heritage said finding a site for a memorial to the Mt Erebus victims was a complex task.
Ministry spokesperson Glenis Philip-Barbara said she understood people's frustration.
"I mean, really, we're asking them to commit to help build and care for a national taonga, which will have a life of more than 100 years. It's a big ask, and a huge consideration."
Philip-Barbara said feedback from the Erebus victims' families would be taken into account.
Another family member, who preferred not to be named, had told RNZ they were looking forward to seeing a National Erebus Memorial constructed on a site that had a strong sense of spirit.
They said it should also be a place where people could gather to reflect on the gravitas of the crash, the impact it has had on the families, search and rescue personnel and the learnings from it that were benefiting those who had come after.
There should be an underlying element of journeying to the sky, as the passengers were 45 years ago, the family member said.
