While Mr Key last week said he knew Mr Fletcher only "vaguely" since their school days, and couldn't recall particular occasions when he'd met his old friend in recent years, Mr Rennie confirmed he and Mr Key discussed Mr Fletcher in 2009.
That was in the context of bringing back expatriate New Zealanders who had performed well in public sectors overseas to fill public sector chief executive roles.
Mr Key was positive about that and told Mr Rennie about Mr Fletcher, "and he told me about the nature of his knowledge of Mr Fletcher".
However, Mr Rennie said he was "surprised" when after discarding a shortlist of four potential candidates for the GCSB job and discussing Mr Fletcher as a potential candidate, Mr Key contacted his old friend.
On Wednesday Mr Key told reporters that at that meeting he told Mr Rennie he would call Mr Fletcher and another prospect identified.
However, Mr Rennie said he couldn't recall Mr Key telling him that.
If Mr Key had said he intended calling Mr Fletcher, Mr Rennie said, "I would have suggested that I do it".
"To avoid any concerns about perceptions I think it would be easier for me to do it," he told National Radio.
Even so, he didn't believe there was a huge issue with Mr Key having made the call and the process of appointing Mr Fletcher was "a robust one".
But Labour deputy leader Grant Robertson said Mr Key's call "absolutely did change the process".
"He clearly wanted Mr Fletcher in his inner circle - he's understated and diminished the nature of his relationship with Mr Fletcher for a week. But what this shows is he clearly had Mr Fletcher in his mind and clearly wanted him in this job and I believe has intervened in this process in order to get him into this job."
Labour yesterday called for an Auditor General's inquiry into the appointment process and has laid a complaint with Parliament's Speaker that Mr Key misled the House with his initial comments about his role in the selection process.
Mr Key yesterday said he would release former Cabinet Secretary Rebecca Kitteridge's report on the GCSB in two weeks' time which would identify "quite significant" and long-standing problems within the bureau.
"They are issues that were there under Mr Ferguson and others and that shows you that just having a military or defence background actually hasn't delivered the robustness of that organisation that New Zealanders would expect."
He rejected Labour's claims he had misled Parliament and the public over the affair.
Mr Key also revealed there were other instances in which he had directly approached people to apply for roles but would not say who they were or what the roles were.
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