The investigation, reported by Fairfax Media, quoted unnamed special forces insiders saying some Australian troops engaged in the "unsanctioned and illegal application of violence on operations" with "a disregard for human dignity".
The report, which Fairfax said was compiled by defense department consultant Samantha Crompvoets, concerned operations by Australian Special Air Service troops and other elite commandos deployed alongside US and allied forces in Afghanistan following the September 11, 2001, terror attacks, AFP reported.
It described a dysfunctional military organization rife with distrust of senior leaders and competition between different elite units.
"Even more concerning were allusions to behavior and practices involving abuse of drugs and alcohol, domestic violence, unsanctioned and illegal application of violence on operations... and the perception of a complete lack of accountability at times," the report is quoted as saying.
The Defense Force declined to answer specific questions about the leaked report, but told Fairfax it was taking "all allegations about Australian Forces seriously" and would be making recommendations based on the findings of the inquiry.
Foreign Minister Julie Bishop also declined to provide details as "there is an investigation underway".
The opposition Labor party on Friday described the revelations as "deeply concerning" and said subject to national security concerns the report should be made public.
"Our soldiers, particularly our special forces, work in difficult and complex environments," shadow minister for defense Richard Marles said in a statement.
"It's important that we know, as a country, that they're doing it in a professional and legal way."
Government parliamentarian and former SAS member Andrew Hastie said the allegations "should be taken seriously".
"We need a free media reporting on all issues that are relevant to the public interest," he told ABC radio, declining to go into detail about the accusations.