Carwyn Jones has asked the Welsh Government's top official to begin setting up an independent inquiry to examine his handling of the Carl Sargeant case.
A spokesman for the Welsh First Minister said Mr Jones believes a senior QC should carry out work to examine his "actions and decisions" in relation to the former assembly member, who was found dead on Tuesday.
Mr Sargeant, 49, is understood to have taken his own life four days after being removed from his role as cabinet secretary for communities and children and suspended from the Labour party over allegations of "unwanted attention, inappropriate touching or groping".
A spokesman for Mr Jones said: "Further to the First Minister's comments yesterday about the need for independent scrutiny of his actions and decisions in relation to Carl Sargeant, he agrees that there should be an independent inquiry and it would be proper to ask a senior QC to lead that work.
"To ensure this happens separately from his office, the First Minister has asked the Permanent Secretary to begin preparatory work for this inquiry, and to make contact with the family to discuss the terms of reference and the identity of the QC.
"It is our understanding that such an inquiry should not take place before the outcome of a coroner's inquest - but we will take further advice on this matter."
Mr Jones had been under mounting pressure to launch an independent inquiry, with Mr Sargeant's family adding to the criticism shortly before the First Minister's announcement.
Mr Sargeant's family said there had been "serious failings" in the way the situation was handled.
Welsh Tory leader Andrew RT Davies and figures from within Mr Jones' own party had called for the First Minister to announce an investigation.
In a statement released through solicitors, Mr Sargeant's family said an inquest into his death would not be able to establish the full picture.
"An independent inquiry will ask all the questions that need to be asked and have not been answered and will determine the reasons for the serious failings in following the correct procedures, practices and protocols, and the reasons for the complete abdication of responsibility and duty of care that was owed to Carl," the statement - reported by the BBC - said.
Former minister Leighton Andrews has claimed that Mr Jones knew that Mr Sargeant was "fragile" before he sacked him.
He has also said the atmosphere in the Government had been "toxic" with "minor bullying, mind-games, power-games, favouritism, inconsistency of treatment to different ministers, deliberate personal undermining" and "Carl was unquestionably the target of some of this behaviour".
In letters to Mr Jones and the Welsh Government's Permanent Secretary Shan Morgan, Tory leader Mr Davies set out his calls for inquiries.
He told the First Minister that an independent inquiry should be held into his handling of Mr Sargeant's dismissal, with a separate probe into Mr Andrews' allegations about the culture in the government between 2011-16 "of which you were alleged to have been aware but failed to address".
In his letter to Ms Morgan he said: "These concerns significantly undermine public confidence in the Welsh Government and need to be addressed as a matter of urgency.
"And for the sake of the wellbeing of Welsh Government ministers, advisers, officials and staff, I would invite you to investigate these allegations immediately and, if necessary, by an impartial third party."
See full story in the Leader