The family of Carl Sargeant has criticised Carwyn Jones' call for an independent inquiry to examine his own "actions and decisions" in the lead up to the death of his colleague.
A spokesman for Wales' First Minister said he believed a senior QC should look into his handling of allegations against the former assembly member, who was found dead on Tuesday, but said it will not take place before an inquest.
However, the family of Mr Sargeant, 49, said asking the Permanent Secretary to start preparations for a probe meant it would not be truly independent.
In a statement they said: "The inquiry must be established by a body that is fully independent of Welsh Government.
"The Permanent Secretary reports directly to the First Minister and is therefore not independent.
"We believe that a truly independent body must also be responsible for agreeing the terms of reference and appointing the chair and secretariat for the inquiry."
Mr Sargeant is believed to have killed himself four days after being suspended from the Labour Party and removed from his role as cabinet secretary for communities and children following claims 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."
But Mr Sargeant's family said there were "serious failings" with the handling of the case. They also said a coroner's inquest would not be able to unveil the complete picture.
They said: "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."
It comes after former minister Leighton Andrews claimed Mr Jones knew his colleague was "fragile" before sacking him.
He also spoke of a "toxic" atmosphere in government rife with "minor bullying, mind-games, power-games and favouritism".
Friday's announcement comes following pressure from Welsh Tory leader Andrew Davies, who also called for an inquiry into the culture within government.Let's