The Prime Minister John Key says he has no regrets about calling Ian Fletcher to suggest he apply for the job as head of the electronic spy agency.
State Services Commissioner Iain Rennie said on Thursday he was surprised the call about the position at the Government Communications Security Bureau was made, and in hindsight it would have been better if the commission had called Mr Fletcher instead.
Mr Key has also disclosed he has approached people about other senior jobs within the public service but will not say which ones. He continues to reject criticism he was wrong to call Mr Fletcher.
Mr Rennie said the recruitment process for the head of the GCSB was absolutely above board. However, he said he regrets that it was Mr Key that rang Mr Fletcher, not himself.
The State Services Commissioner said perceptions of cronyism can occur whenever a minister suggests someone for a job and it happened under the previous Labour-led Government.
Labour Party deputy leader Grant Robertson believes in this case Mr Key went a step too far.
Applications for the job at the GCSB opened in May 2011. The Prime Minister said on Wednesday that a shortlist of four candidates was rejected by the State Services Commissioner and it was at that point he rang Ian Fletcher and one other person to see whether they were interested in applying.
The Labour Party on Thursday called on the Auditor-General's Office to investigate the process used to appoint Mr Fletcher.
Deputy leader Grant Robertson told Radio New Zealand's Morning Report programme on Friday questions remain about the recruitment.
Mr Robertson said Mr Key cut across a recruitment process agreed with the four candidates shortlisted for the job.
He said the Prime Minister's only official role should have been in recommending the final candidate once the process was complete.
Meanwhile, Mr Key is promising that the GCSB faces plenty of change as a result of the report into the agency by Cabinet Secretary Rebecca Kitteridge.
He said the report identifies significant problems in the organsation and a need for a change in management. The report will be released when the Prime Minister returns from China in two weeks.