Former Defence secretary and ASIO boss, Dennis Richardson, was selected to inquire into Home Affairs' management of offshore processing in July 2023.

The Home Affairs Minister Clare O'Neil announced the review after Nine reported allegations that contractors engaged by the department were suspected of systemic misuse of taxpayer money in Nauru and Papua New Guinea.

Mr Richardson's review was provided to government in October 2023, but not published until Monday.

He found that Home Affairs had lacked proper due diligence in its procurement process and that information sharing between agencies was inadequate, and that it had contracted companies which were under investigation by the Australian Federal Police, as well as an enterprise suspected of corruption.

The review noted that it "did not come across any matter of deliberate wrongdoing or criminality", and that it did not find any evidence of ministerial involvement. Opposition Leader Peter Dutton was the Immigration Minister during some of the time in focus.

But Greens senator Nick McKim, speaking in Senate estimates on Monday morning, was concerned the department had not actively identified public servants involved.

Ms Foster said this posed a difficulty given "many areas of the department" were involved in the procurement processes scrutinised by the review.

"As [Mr Richardson] articulated it, to me, there were many areas of the department involved," she said.

"So there was, you know, an overarching procurement process, there was the regional processing team itself executing the contract, there was an intelligence area who was or wasn't feeding information into the contracting process.

"And I don't want to verbal him, but my understanding is that he did not feel that it was productive, to go back in time and seek to unravel that.

"He felt that - certainly in terms of he and I talking about my approach going forward - that I should focus on making sure that we learned from those mistakes and got them right in the future."

But Senator McKim pressed Ms Foster on why the department was not identifying and reprimanding individuals.

"But if none of us know, or can find out, who was actually responsible for these decisions, that's an egregious failure of process inside the Department of Home Affairs, isn't it?" he asked.

Ms Foster noted that Mr Richardson "did not identify any deliberate wrongdoing or criminality" in his findings.

Senator McKim pressed on: "But that doesn't preclude utter incompetence, Ms Foster, does it?"

"I don't believe, and again, I'll have someone check the report, that there was any finding of utter incompetence," the secretary responded.

Ms Foster also denied that the review had produced "a scathing report", as Senator McKim described it.

"I would actually characterise it as a report which acknowledged the shortcomings of the past and gave us a sense not only of confidence in the remedies that the department had taken over years," she said.

"But also made a couple of other specific recommendations where we could improve our processes which were acting on."

Senator McKim and Senator James Paterson, the opposition's spokesperson for Home Affairs, expressed frustration over the timing of the report's public release.

The Home Affairs Minister's office sent the report out about 6.30am on Monday, just hours before the first hearings began.

Labor senator Murray Watt, representing the Minister for Home Affairs, said the government had been considering the findings since it received it in October.