Finders are asked to take the objects to a museum within 28 days, where they can be assessed and the ministry notified.
Under the Protected Objects Act all such items belong to the Crown until the ministry decides what care and custody they need, Evans said. Museums will often hold them until that is decided.
The ministry looks for traditional owners for them - usually iwi or hapū from the area where they were found.
Claims of ownership for them can be made until February 3, and the ministry is also contacting possible owners directly.
If only one claim is made and it seems valid, the ministry will apply to the Māori Land Court for an order determining ownership and custody.
If conflicting claims are made, the ministry works with claimants to find a resolution.
It will continue to work with the potential claimants and interim custodians of these two objects, Evans said.