Attorney-General Mark Dreyfus will present a draft bill for the integrity body to the Labor caucus for approval next Tuesday before introducing it to parliament on Wednesday.

Patrick Gorman, the assistant minister to the prime minister, said the coalition had done nothing in 10 years to get the laws through parliament, but Labor could do it within 10 months of taking office.

That timing would mean the laws passing parliament by March – 10 months after the May election – despite Labor promising during its campaign to legislate the commission by the end of 2022.

“We’ll get it done within the first 10 months of this government,” Gorman told ABC radio on Tuesday.

He said while the government would like to see the bill passed by the end of the year, it would need to clear the Senate where Labor doesn’t hold a majority.

Senate procedures and committees may also hold up the legislation passing before December.

“In terms of timelines, I don’t want to step through every piece of the legislative journey,” Gorman said.

“But we think it’s possible that by the final sittings in early December, this could be the law of the land.

“But I’m being appropriately respectful of the parliament, both chambers, to make sure that we get this right.”

Labor will require the support of the Greens and one crossbencher to get the bill through the Senate if the coalition votes against it.

The Liberal-National coalition proposed a Commonwealth Integrity Commission, which was the subject of public consultation, but did not bring a bill to parliament.

The Labor bill would set up a body known as the National Anti-Corruption Commission, which would investigate federal ministers, public servants, statutory office holders, government agencies, parliamentarians and personal staff of politicians.

It would have the power to investigate allegations of serious and systemic corruption that occurred before or after its establishment, as well as hold public hearings where the commission determines it is in the public interest to do so.

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.