They had been “embraced” by Maori, with whom they shared similarities as people affected by colonisation, he said.
They were also both warrior people, in the past and in their present day fight for rights.
A shield and boomerang he had made and gifted during the ceremony represented this.
“The artefacts are symbols [of] a very fighting people, a very strong people.”
It was also a promise of the bond between two first nations.
Museum director of collections and research Robert Morris said it was the first repatriation of Australian aboriginal items from New Zealand, along with items returned by Auckland Museum earlier this week.
It was an important step in the decolonisation process for museums, he said.
In the past there had been a lack of understanding of the spiritual and ancestral significance of objects taken.
He hoped this could lead to the return of Maori artefacts to New Zealand in the future.
Australian Minister for Indigenous Australians Linda Burney said the return of the artefacts was a significant moment for the Warumungu people.