A complicated case of 'whodunnit' has erupted in the Senate, with the federal government insisting it had no role in the online publication and subsequent removal of a report recommending sweeping changes to Australia's military justice watchdog.

A review into the Office of the Inspector General of the Australian Defence Force, which investigates misconduct and deaths within defence, was published online by the royal commission into defence and veteran suicide.

It recommended moves to improve the organisation's independence, amid concerns it's too closely linked to the military's top brass and is hamstrung in its investigations.

The final report had been provided to the inquiry by the government, as part of its investigation into culture within the ADF.

Repeated demands from independent senator Jacqui Lambie and Greens Senator David Shoebridge to the government to publicly release the report had been denied for months.

But the pair discovered the report had been included in bundles of other evidence on the royal commission's website on Tuesday.

Soon after, it suddenly disappeared following inquiries from their offices.

Senator Lambie and Shoebridge accused the government of trying to cover it up on Wednesday, which the government denied.

"I'm advised there was no direction or request from the government, from the deputy prime minister, his office, the Department of Defence, or the IGADF to the royal commission," government Senate leader Penny Wong told the upper house on Thursday.

"On two separate occasions, the Commonwealth solicitors advised the royal commission's solicitors the report had not been published, and requested the royal commission carefully consider its use of the report, including any publication pending the government's review of the report."

She said the royal commission's 'official secretary' made the decision to remove the report, independent of government.

"The government remains committed to improving our military justice system and the culture of the Australian Defence Force, because we owe nothing less to the men and women of the ADF and our veterans," Senator Wong said.

The report is now public, and Senator Shoebridge fired back.

"The royal commission ended Monday last week," he told the Senate.

"There's an employee of either the Attorney General's Department or Prime Minister and Cabinet, not sure, who purports to call themselves the secretary of the royal commission, purporting to make a statement on the part of the royal commission, when the royal commission ended.

"I'm going to call bulls##t on that."

He quickly withdrew the final comment, but insisted the now former royal commissioners themselves wanted the report public.

Senator Lambie accused the government of "hitting the panic button."

"What a debacle this has been," she said.

The federal opposition also seized upon the situation.

"This has been a most unnecessary and most counterproductive bungling of these matters by the Albanese government," Opposition Senate leader Simon Birmingham said.

"What we have seen through their mishandling, mistakes and bungling of the handling of these sensitive reports is an undermining of already shaky confidence and trust in the IGADF, and an undermining of confidence in the government's commitment and ability to address the serious issues facing Australian veterans."