Dennis Richardson to lead inquiry into Home Affairs bribery allegations

Meanwhile, the Greens have called for a royal commission into offshore detention, with the party's home affairs spokesperson Nick McKim saying anything less would be "another bipartisan stitch up that ends up in a whitewash".

Tensions reached a boiling point in Senate Question Time, during which Mr McKim - in a heated exchange with Senator Murray Watt - said the government's inquiry would result in a "cover up" and asked whether Labor would stand down current Home Affairs Secretary Mike Pezzullo.

All eyes are on the Mr Pezzullo and the Home Affairs Department following an investigation by Nine newspapers and 60 Minutes, which revealed that several contracts related to Australia's offshore processing regime allegedly helped funnel millions to local politicians in Nauru and Papua New Guinea.

The Australian Federal Police subsequently revealed that it had briefed then home affairs minister Peter Dutton in 2018 on an investigation into Sydney-based businessman Mozammil Bhojani over suspected bribes to Nauruan politicians.

The following month, the Department of Home Affairs entered into a new contract with Bhojani's company Radiance International.

Senator Watt, representing the Home Affairs portfolio in the Senate, said following the "concerning allegations", the government had received assurances from the department that all contracts and payments were being made "according to law under this government".

Senator Watt refused to be pinned down on questions as to whether it would agree to a royal commission into immigration detention, instead pointing to the government's inquiry led by Mr Richardson, announced by Home Affairs Minister Clare O'Neil just moments before Question Time.

The former Defence Department and Department of Foreign Affairs and Trade secretary is one of Canberra's most distinguished public servants, having served a dozen prime ministers over five decades.

Senator Watt said that the government's inquiry would investigate "any integrity concerns about contracting arrangements regarding regional processing", but would "not canvass the policy of regional processing itself".

Senator McKim accused the inquiry of being too narrow in scope, alleging that it will result in a "cover up, not the answers we need".

But Senator Watt responded that the Greens senator was making allegations in his "usual, over-reaching style", adding that he had full confidence in Mr Richardson "as one of the most esteemed public servants this country has produced".

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Senator McKim, speaking to reporters earlier in the day, said that a royal commission was the only acceptable response to "a humanitarian catastrophe that was enabled by systemic and serious corruption".

"These are highly credible and extremely serious allegations of systemic corruption," he said.

"Offshore detention has been one of the darkest and bloodiest chapters in our country's history, and there is no chance that we can write a conclusion and make sure that it never happens again until we get a royal commission."

The opposition leader fronted journalists in parliament on Monday morning over the growing controversy, offering to participate in any integrity inquiry while adding that the allegations were "a complete nonsense".

"If there are matters to be referred to the minister has legitimate concerns around the conduct of any individual, I would be happy to co-sign a letter with the Prime Minister to refer to them to the NACC and allow them to conduct their own investigation," Mr Dutton said.

Mr Dutton said that he had no memory nor record of receiving the briefing from the Australian Federal Police, adding that, as minister, he had "no involvement in procurement".

Mr Dutton also accused Minister O'Neil of being at "loggerheads with the secretary of her department" Mike Pezullo, offering that Mr Pezzullo was is a "first-class public servant".

The Canberra Times does not suggest Mr Dutton was involved in the contract decision.