But items from the museum's collection could be displayed at the redeveloped gallery while on loan.
Cr Jim Hopkins told a Waitaki District Council meeting he wanted more information on a call from Waitaki Mayor Gary Kircher to ''accept back all of the artefacts that came from Waitaki and are being kept at Otago Museum''.
Mr Kircher was not present at the meeting, but in reviewing his report, Cr Jim Hopkins requested council chief executive Fergus Power delegate someone to determine what artefacts Otago Museum had that were ''ours'' and ''what exactly we can get back''.
This week Otago Museum collections and research director Robert Morris said repatriation of artefacts was unlikely.
''Most of the claims of repatriation that we manage are with cultural material from various iwi,'' he said.
''It would be remiss of us to act in contravention of the original intentions of the donors, quite frankly.''
However, Otago Museum would be happy to loan artefacts from its collection to an upgraded Oamaru museum.
Yesterday, Mr Kircher said his comments were made in relation to a regional funding issue for the museum.
Under a 2018-19 proposed budget, $4,267,826 funding for the museum come from local council contributions. The funding formula called for the Dunedin City Council to pay 93.7%, or $3,998,952.90; Central Otago District Council to pay 0.63%, or $26,887.30; Queenstown Lakes District Council to pay 0.72%, or $30,728.35; Clutha District Council to pay 3.69%, or $157,482.77; and the Waitaki District Council 1.26%, or $53,774.61.
Clutha agreed to pay only what it considered it was legally obliged to, $121,000.
Clutha Mayor Bryan Cadogan disputed the funding formula and asked for fairness when territorial authorities were paying for Otago Museum ''to preserve our heritage ...''.
Mr Kircher said he made the comment the district would ''accept back'' artefacts in light of a suggestion Waitaki could pay more.
He pointed out Waitaki council was paying close to $1 million a year to the [North Otago] museum, gallery and archive and working on a $6 million upgrade, which was a major undertaking.
''And we want to look after our own stuff, in our own place, and tell our own stories. That's what it's all about.
''... it just came up when this whole argument about 'we should be paying them to look after our artefacts' - I was just simply making the point that we were quite happy to look after our own artefacts ... and we'll certainly do that in a co-operative way.
''And we'll certainly carry on paying.''
