The assembly's first minister has said he broke no rules in blocking the appointment of a prominent barrister as the assembly's counsel general.
Mr Morgan said he deplored the leaking of the candidates' names
In a statement to the assembly on Tuesday, Mr Morgan told AMs he did not want the job to be given to Gerard Elias QC because of his links with hunting and freemasonry.
But opposition parties remained unconvinced after he confirmed that former Labour Lord Chancellor Derry Irvine was a referee for Malcolm Bishop QC, Mr Morgan's favoured candidate.
Opposition parties said that added to concerns that his interventionism was politically motivated - a charge Mr Morgan denies.
BBC Wales' Dragon's Eye programme revealed last week that Mr Elias was recommended for the £140,000-a-year job by an independent panel.
It has been claimed that Mr Morgan blocked the recommendation because he wanted another barrister with strong Labour connections.
Mr Morgan said Mr Elias' advice would not have 'untrammelled authority'
But the first minister has said the Civil Service Commissioners had found no breach of the recruitment code and he had said suggestions he had been subject to Whitehall pressure were "pure invention."
Speaking at the assembly, Mr Morgan said he deplored the leaking of the two candidates' names to the media but went on to explain his opposition to Mr Elias' appointment.
He told the AMs gathered in Cardiff Bay that legal advice from a counsel general prominently associated with hunting and freemasonry "would not carry the necessary stamp of untrammelled authority throughout the assembly".
He added that he was instigating a leak inquiry to find out how the names of the candidates had reached the public domain.
He said: "That they as individuals and their candidacies should have been subject to public comment in this way is a matter of shame to public life in Wales."
But opposition parties argued that suspicion remained about Mr Morgan's actions due to the fact that his favoured candidate had close links with the Labour party.
The first minister said there was no evidence to back the accusation that his intervention was politically motivated.
Conservative Assembly leader Nick Bourne said that Mr Elias could surely have relinquished the links with hunting and freemasonry had he been appointed, in the same as the first Counsel General Winston Roddick resigned from the freemasons.