Public servants at Centrelink have been threatened with disciplinary action or even criminal prosecution as their bosses at the welfare agency try to stem the flow of internal leaks about the agency's "robo-debt" campaign.

Several workers have gone public about the debt recovery debacle since the controversy emerged last month and now Centrelink's parent department, Human Services, has issued a stark warning to its 36,000 staff about the consequences of leaking.

The department, which has gone to extraordinary lengths and expense in the past to track down and crush internal dissent, issued its latest warning on Tuesday after several media stories featuring insider accounts of the data matching program's failings.

The controversial program will not face the scrutiny of the Commonwealth Auditor-General, it was confirmed on Wednesday, with A-G Grant Hehir saying he does not want to double-up on the inquiry underway by the Commonwealth Ombudsman.