The Ministry of Culture and Heritage says it is pleased with the actions of people who found adze heads and notified their local museum.
The two blades were found at Shag Point in Otago and at Papatowai, near the Catlins in Southland.
Adze blades were typically used for woodworking and were often made from greenstone, but one of these appears to be of grey coloured stone.
They were handed in to Otago Museum which disclosed the matter to the Ministry, which has since begun a process of trying to trace their ownership.
A Ministry official said the adzes appeared to be very old but no exact age is known at this stage.
He said they could have significant cultural value to relevant iwi.
The official could not say what value they would have but said the law required them to be handed in, so their ownership can be traced.
He said ownership sometimes had to be settled by the Maori Land Court in disputed cases.