Mr Puna, who is from Manihiki, agreed to give the landowners just under US$26,000 during Te Maeva Nui celebrations so they could go shopping before returning to the island.
The Government has previously said that the payment was made after the landowners threatened to vandalise the two solar plants on the island if they were not paid.
In a statement from his office Mr Puna expressed surprised that the early payout had sparked a police complaint.
Businessman George Pitt made the complaint and says the Manihikians committed a criminal offence and were 'aided and abetted by the prime minister'.
He says both the Manihiki group and prime minister need to be charged.
Mr Puna's press secretary says the prime minister will not yet comment on the claim, except to say he 'stands by the urgency of the decision that Cabinet needed to make to diffuse an unstable situation in Manihiki'.