Kirk Ramsay left his post at the Glasgow further education college on Tuesday after criticism from Michael Russell over the recording, using a pen device, of a private meeting.
Mr Ramsay distributed the recording and Mr Russell demanded he resign, which he did citing an "unwarranted personal attack on me by Michael Russell MSP".
Allegations of bullying from MSPs emerged and Mr Russell refused to apologise.
After the convener of the education committee, SNP MSP Stewart Maxwell, refused a request to call Mr Russell back to the committee, Labour, Conservative and LibDem MSPs demanded an inquiry. Mr Maxwell also defended the cabinet secret-ary, leading to questions about his impartiality.
Mr Ramsay supported calls for a parliamentary inquiry, adding: "The minister over-reacted, grossly over-reacted."
A letter signed by two Labour MSPs – Neil Bibby and deputy convener Neil Findlay – Conservative MSP Liz Smith and LibDem MSP Liam McArthur expressed concerns about impartiality.It said they were concerned about a "culture of secrecy, bullying and intimidation, characterising the Cabinet Secretary's relationship with parts of the college sector".
Deputy convener of the education committee Neil Findlay said: "I am genuinely shocked by the partisan way in which Mr Maxwell is behaving as convener.
"He alone has decided to block any attempt by the committee to look into this. I hope Mr Maxwell remembers his primary job as convener is to hold the SNP Government to account."
Mr Maxwell said: "A parliamentary inquiry is about making sure we establish the facts: the facts aren't in dispute here. Mr Ramsay's position became very difficult because he secretly recorded a meeting, then distributed material to others, those are the facts."