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The discovery was made on December 25 on the side of Mt Ngāuruhoe.
"We always go hiking over Christmas," said David Hallberg, who was on the Tongariro Circuit with his partner when they made the find.
He said the box contained an engagement ring and a wedding band, which could have been on the hillside for years.
"They have been under the ice and gravel for a long time, they are deformed and somewhat faded."
The engineer from Northland was keen to find out who they belonged to. He took the two rings to the Doc warden and shared their find with the other hikers at the hut.
"Everyone thought it was very cool," he said, sharing some of the speculations as to how they came to be left on the side of the mountain.
"I hope she still said yes!"
A spokesperson for Doc says the Tongariro Visitor Centre team is aware of the discovery.
"The Tongariro Visitor Centre does keep a log of lost property items handed in by people," they said.
"However, we haven't had any reports or requests relating to the rings. It would be great to see them returned to their owner."
For valuable lost property items – like jewellery - the centre asks that they be handed in to NZ Police.
The National Park Police Station said it was not aware of any reports of similar missing items.
One clue to the owners' identity is that the box is from a well-known American jeweller, not found in New Zealand.
In a twist straight out of the Lord of the Rings he saw there was something written on the bands.
"They have a inscription in them, but I don't want to say what, so the rightful owner can claim them."
He hopes that whoever they belong to might have friends or relatives in New Zealand, and can get in touch.
Hallberg, who is a fan of the Tolkien films, says he feels duty bound to find the original owners.
"I would love to return them to their owner and hear their story of the lost rings on 'Mount Doom'".
Doc asks that hikers making the detour to the mountain respect the sanctity of Ngāuruhoe and not tramp to the summit.