Intelligence agencies have admitted making a second secret recording of a seven-hour interview with asylum-seeker Ahmed Zaoui.
The existence of the audio tape was only revealed when Prime Minister Helen Clark questioned the competence of security services.
Part of a video recording of the same interview has mysteriously disappeared.
Those people who say Zaoui is a legitimate refugee said the circumstances surrounding the tapes prove that the secret service is withholding vital information.
Former Race Relations Conciliator Gregory Fortuin said he is suspicious.
"Obviously matters of national security are important but nobody can be a law unto themselves. The tapes appearing and disappearing and reappearing almost sounds like the people in South Africa who died and it was said they tripped over a piece of soap or something," Fortuin said.
The Greens' security and intelligence spokesman, Keith Locke, called for more information to be made public.
"We can't accept that it takes the threat of a Prime Ministerial investigation for the SIS to come clean. They should come fully clean. They should provide all the information from their interviews on Mr Zaoui," Locke said.
But Immigration Minister Lianne Dalziel said secrecy is paramount if New Zealand is to continue to receive information from foreign intelligence services.
"It comes down to whether New Zealanders believe that we should be part of the international intelligence community. Whether New Zealand should be able to receive intelligence from other intelligence agencies around the world because much of the information is provided on the basis it is classified information and that therefore must be confidential, she said.
NZ First Leader Winston Peters said the Zaoui case is wasting taxpayer dollars. He believes Zaoui should be sent home immediately.
"Why did he bypass all those Muslim countries to come to New Zealand, if it were not for the fact we are the world's softest touch," Peters said.