The museum, which is notable for its 1990 pyramid-shaped building constructed over the original 1942 museum, has been closed since 2018 due to safety risks but an advocacy group has been campaigning for it to reopen.
Friends of the Southland Museum and Art Gallery Museum group member Lynley Dear said she wanted to "put an end to the slow death" of the "unique heritage institution".
"Theft is a crime and our Museum and Art Gallery has been stolen from us."
She was one of about 80 people attending the meeting on Monday evening.
Guest speaker, quantity surveyor Lindsay Buckingham said despite the building being deemed earthquake-prone, the Building Act did not require it to close.
He also said the building had not been "officially declared" earthquake-prone.
"The building could and should be reopened immediately, as it remains in full compliance with the Building Act as long as the rectification work is completed within the 25-year period. "
Colin Anderson, who worked at the museum in 2007, said the pyramid building had a lot of structural issues and he supported the construction of a new one.
Crs Nobby Clark and Toni Biddle, the deputy mayor, were present at the meeting in a personal capacity.
Cr Biddle took the opportunity to clarify some points made by attendees, but chairman Bob Simpson said she could not interrupt others.
"If you shut up, you will have the opportunity to talk."
People argued he was being rude, and some time later, he invited Cr Biddle to talk.
She said she went to the meeting in the hope of finding a pathway forward.
"But sadly, what I heard so far has been a reiteration or relitigation of previous decisions that will definitely get us nowhere."
Cr Clark said the best way to move forward was to wait for the results of the motion she proposed this month, when she asked the council’s chief executive Clare Hadley to report back in five months with details on all the options around the museum, including the possibility of strengthening it.
The debate ended with the approval of a motion by the group requesting the council to do a geologic report and investigate the possibility of reoccupying the building.
