Prime Minister John Key says he is taking advice about a request from the daughter of Jeannette and Harvey Crewe to order an investigation into their unsolved killings in 1970.
Rochelle Crewe's request comes a week after police said they would not reopen the investigation, but would review their case files.
Mr Key said the matter is very complex and he is taking advice on it.
Arthur Allan Thomas was convicted twice of the Crewe's murder and later pardoned. No-one else has been tried.
A Royal Commission of Inquiry raised serious questions about the police investigation but no officers were prosecuted.