Section 7 of the Crimes Act notes that any person who receives or communicates a secret document without permission has committed an indictable offence and faces up to seven years in prison.
Opposition Leader Anthony Albanese,who was being interviewed alongside Mr Dutton,was given an opportunity to say whether he believed police action against reporters should be dropped,but said it was a matter for the government.
"Quite clearly the government needs to show leadership on this issue,"he said.
Mr Albanese has previously challenged Attorney-General Christian Porter to explain whether he stood by his claim that there was"no evidence"journalists were the focus of law enforcement action.
The Sydney Morning Herald andThe Age this weekrevealed the AFP approached Qantas in March seeking details on two flights taken by one of the two ABC reporters who received and published top-secret government material containing allegations of misconduct by Australian troops in Afghanistan.
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A document recounting the exchange between the AFP and Qantas is headlined"Statement in the matter of R v Daniel Michael Oakes",suggesting police could be building a case against the reporter in addition to pursuing the Defence whistleblower who has already admitted to leaking the information.
In addition to the possible case against Oakes,emails obtained under freedom of information laws show that Smethurst could also be prosecuted.
A detective sergeant from the AFP's"sensitive investigations"unit emailed communications staff on the morning after the raid on Smethurst's home to thank them for their service.
One staff member wrote back:"Reporting hasn't caught up on the publishing offence - many still think she's just doing her job."
Asked last month whether it was a crime to publish leaked secret documents,acting AFP commissioner Gaughan replied:"Yes,it can be",but noted there might be public interest exemptions under federal law.
"I'm not going to rule in or rule out anyone subject to further charges,"he said.