Peter Dutton insists it was Victoria Police which invited the federal agency to participate in the weekend Operation Fortitude, which was to take place in Melbourne, and visas would only be checked if referred.
"The way it's been blown up is regrettable and I think frankly the hysteria that Bill Shorten and others have shown demonstrates a lot probably more about them than the officers," Mr Dutton told 2GB radio.
The minister admitted a press release, which said officers would talk to people who crossed their path, was poorly worded and a mistake.
He defended the Victorian commander who looked at the statement as a "good man".
In his first public comment on the bungled operation, Mr Dutton said he was sick over the weekend and didn't get out of bed to address the media.
Opposition immigration spokesman Richard Marles has told Sky News he has written to the Auditor-General requesting an examination of training for Border Force personnel.
He accused Mr Dutton of eroding public confidence in the agency by keeping quiet.
Labor and the Greens are demanding an explanation from Mr Dutton about the intention of the cancelled operation.
The parties want him to take responsibility and explain the intention of the operation, which the agency first said would include talking to people that crossed its path.
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