The MEAA house committee sent an email to about 1,000 members on Monday detailing the threat and calling for a collective response.
Robinson, who joined the ABC as director of news just four weeks ago, and national and digital news boss Lee Glendinning met with Slezak last week to raise concerns about his conduct. According to the email, the pair told Slezak he may have breached the ABC's external work policy and code of conduct over an opinion piece he wrote in The Australian Financial Review. They refused to rule out the possibility of disciplinary action or dismissal.
In the article, Slezak argued against plans to limit publicly available information about company directors in Australia. He wrote that the Australian Institute of Company Directors and its chief executive Mark Rigotti was using the Bondi terror attack as a "shield" to help push forward long-held changes on the issue.
The union's house committee has called a meeting of members for Tuesday and demanded that ABC management rule out any action against Slezak. It called on management to ensure union representatives can undertake legitimate advocacy in future "without intimidation or reprisal". The email warned that any attempts to intimidate elected staff representatives "must be met with a collective response from the members they represent".