Leighton Andrews alleged First Minister Carwyn Jones knew of the allegations but nothing was done.
Mr Jones met Labour AMs on Thursday to explain how he handled conduct allegations against Mr Sargeant.
Found dead four days after being sacked from the cabinet on Friday, it is understood Mr Sargeant took his own life.
Mr Jones dismissed him as communities secretary following claims of inappropriate behaviour made to the first minister's office.
The Alyn and Deeside AM had vowed to clear his name but said he did not know the details of the allegations.
Mr Jones is expected to make a statement from Welsh Government headquarters in Cardiff on Thursday afternoon, following the meeting with Labour AMs at the Senedd in Cardiff Bay which has finished.
The Welsh Government has declined to respond to Mr Andrews's claims.
There has been criticism of the way Mr Sargeant was treated and his family has called for an inquiry.
Former public services minister Mr Andrews - who alleged "minor bullying" and "mind games" during his time in government - said during the last assembly term the atmosphere "was toxic".
He alleged "minor bullying, mind-games, power-games, favouritism, inconsistency of treatment to different ministers, deliberate personal undermining on occasion".
"The undermining was of ministers, deputy ministers and special advisers," Mr Andrews said in a statement issued on Thursday.
The ex-Rhondda AM said he had raised one particular issue with Mr Jones, of which he had direct evidence, but claimed due process was not followed.
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