Prime Minister John Key also has concerns, saying he is "inquisitive" about the new information received about the Teina Pora case.
However, Mr Key said the Government should stay out of the way until the appeals process is exhausted.
He was asked today if any inquiry into the case should be held, and said there were two paths that Mr Pora's lawyer Jonathan Krebs could take:
"One is obviously an appeal to the Privy Council and the second pathway is one more of negotiation. Our understanding is they're still going down the Privy Council route.
"It's highly unusual for the Police Association to make the moves that they did on Saturday night, but it's best if it's handled by the minister," Mr Key said.
The Police Association joined the call for the independent inquiry into the conviction of Pora, who is serving his 21st year in prison for the rape and murder of Susan Burdett.
"It's about time there was an independent inquiry, especially when senior detectives, who have a great knowledge of the case, start of have their doubts," Association president Greg O'Connor said.
NZ First leader Winston Peter said he thought Pora was innocent.
"This looks like a tragic case. Don't forget he presented himself as a witness at the start and that got the police going.
"They had critical information on the DNA which they should have made available to the defence in his trial and they didn't. That's a serious breach of the rules."
Justice Minister Judith Collins has shut down any calls for an inquiry into the case.
She previously refused questions on the case, but today told media that an inquiry would not be held.
She said an appeal to the Privy Council was likely as Mr Krebs had told her ministry yesterday he wanted to pursue the case.
"That is absolutely his right to pursue and I can't step all over the court system just to score political points or to win a popularity contest."
Ms Collins said today if people had complaints about police, the Independent Police Conduct Authority (IPCA) was the correct body to lay a complaint with.
She said anyone who had an interest in the case should be deciding if they were serious enough to put an application to the IPCA.
"I'm certainly not going to make a comment on whether or not they should be sent there, but it's all very well to make all sorts of allegations, but there is already this authority that was set up not that long ago to look into matters like this."
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