Classified national security advice was sent to just a handful of the nation's most senior officials before it was leaked to the media at the height of a major political dispute over border protection.

The revelation, contained in documents released under freedom of information laws, casts fresh doubt over claims by the Australian Federal Police that it did not investigate the unauthorised disclosure given "the large number of potential suspects".

The leak, which Australia's top spy decried as "seriously damaging" and Labor alleged was orchestrated by the Morrison government to discredit laws to fast track asylum seeker medical transfers, was referred to police by the Department of Home Affairs earlier this year.

The Sydney Morning Herald and The Age revealed in June that police evaluated the referral but opted against launching a full investigation "due to the limited prospects of identifying a suspect".