The Green and Labour parties say if John Key has nothing to hide, he should approve the release of a taped cafe conversation between himself and John Banks.
The National leader has laid a complaint with police on Monday over what he says was a covert recording made on Friday.
Mr Key and the ACT Party candidate met at a Newmarket cafe for a cup of tea, intended to be a public show of support by National of Mr Banks' campaign to win the Epsom electorate.
When reporters were told to leave the cafe after an opening few words from the politicians, a freelance cameraman working for the Herald on Sunday left his microphone on the table. Bradley Ambrose says this was unintentional.
The newspaper was given the recording, but its request to use the material was turned down by John Key's office and the paper says it has decided not to publish the contents for legal and ethical reasons.
However, if made public, the paper says the contents could affect the election result.
Greens co-leader Russel Norman says John Key and John Banks expected that their conversation would be private - but if there is nothing to worry about, the tape should be made public.
"If I was Key, I'd release the tape. But it is at the end of the day their private conversation, and so I can understand why there's a rule around it."
Labour leader Phil Goff says taping the conversation might not have been the right or ethical thing to do, and he is not justifying that.
But he believes Mr Key should put an end to the speculation about what was said and allow the details to be released.
"It was a public event, it was a media stunt. I just say this to John Key: let's stop the speculation, let us hear what the conversation was. Was it about which assets can we connive to sell off next?"
