Opposition leader Peter Dutton says the coalition is negotiating “in good faith” with the Albanian government over the bill to create the National Anti-Corruption Commission (NACC).
The bill will go to the Labor caucus for approval on Tuesday and will then be submitted to parliament.
It then moves to an investigation involving MPs and senators, with a view to being passed by the end of the year or early 2023.
Dutton was a minister in Morrison’s government who proposed a Commonwealth Integrity Commission of his own, but did not bring a bill to parliament.
He told reporters in Canberra on Friday that he had been instructed by the coalition party chamber to discuss the bill with Labour.
“I support the principle,” he said.
“The shape of that and the way we want to work with the government, we’ll comment more on that in due course.”
He declined to specify where the coalition stood on various aspects of the bill.
“Right now we are having discussions… I have spoken to the Prime Minister about the matter and we will continue to do so in good faith.”
Supporters of a national integrity watchdog have spoken of the need for bipartisan support if the commission is to stand a chance of long-term success.
The NACC would investigate federal ministers, civil servants, statutory office holders, government agencies, MPs and personal staff of politicians.
It would have the power to investigate allegations of serious and systemic corruption that arose before or after its creation, and to hold public hearings where the commission determines that this is in the public interest.
While it could make a finding of corrupt conduct, such findings would then be referred to the Australian Federal Police or the Commonwealth Department of Public Prosecutions.
Without the support of the federal opposition, Labor would need the Greens and one cross-bencher to get its bill through the Senate.
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