Napier mayor Bill Dalton said it was not uncommon for museums to have storage off site.
"We currently have, we're looking and working through various options to improve that off-site storage but the likelihood is we will continue to have off-site storage," he said.
"It's a work in progress, we have got more and more of the collection into the building, but we will have some part of the collection that doesn't fit in the building.
"In the meantime I want to stress that the collection is very securely, and properly looked after."
However the continued expenditure to house the collection has riled the New Zealand Taxpayers Union - a group which lobbies on behalf of the taxpayer.
Union executive director Jordan Williams said they had labelled the council's management of the upgrade an "omnishambles", back in 2014.
"Three years ago, the Council said the storage issues were 'undergoing a review to get it fine-tuned'. Now we know the truth, that no one has [lifted] a finger."
"We're hearing more and more from our members in the Hawke's Bay that they are sick of poor performance, waste, and excuses from the local councils. Here's a perfect example of what they are talking about."
Mr Dalton said his "only response to the New Zealand Taxpayers Union is I don't respond to any of the nonsense they talk".
The Napier Library on Station St had been considered for archive storage, but as it had recently being found earthquake-prone, this was no longer an option.
In June, a council-commissioned seismic assessment on their two civic buildings in the Napier CBD found both were an earthquake risk. The library building had measured surprisingly low, at 15 per cent the of the New Building Standards.
"In light of council's wider building and accommodation issues it makes sense to investigate MTG's storage alongside the wider council and library archive storage options," Ms Campbell said.
The initial intention of the MTG Hawke's Bay, as stated in a 2009 fundraising booklet for the upgrade, had been for a facility capable of storing the entire collection "with room left for further growth".
The basement of the MTG building has been converted into storage space, which was hoped would increase the volume of storage on site.