Mr Fletcher's appointment was yesterday compared by Mr Rennie to the 2007 appointment of Clare Curran to the Environment Ministry, under the Labour Government.
The Prime Minister, who claimed to have forgotten about the phone call to Mr Fletcher, has previously said it was unreasonable to expect he remember every phone conversation which took place.
Labour have called for an auditor-general's inquiry into the appointment process, though Mr Key believed the New Zealand public would not find any problems in the appointment process.
"I think they see through it. It went through a very robust process as the state services commissioner said."
A report by former Cabinet Secretary Rebecca Kitteridge on the GCSB is expected to be released in two weeks.
Mr Key would not be drawn on details of the report today, but has previously said it would identify "quite significant" and longstanding problems within the bureau.