Mr Morrison's agreement is needed to ensure Federal Parliament can debate changes to the territory's self-government act, to allow the ACT integrity commission to be able to investigate allegations of corrupt activity by police.

This final hurdle for the integrity commission is due to the territory's police force being a branch of the Australian Federal Police, which the ACT government contracts out from the federal government.

It is understood Mr Barr previously wrote to then prime minister Malcolm Turnbull seeking his agreement, but the issue was not clarified. He then wrote to Mr Morrison about the issue in August, but has not yet received a response.

Despite the lack of agreement to date, final agreement of all ACT political parties on the details of the proposed integrity commission is imminent, ahead of the debate and expected passage of the legislation on Thursday this week.

Resolutions appear to have been reached, or will be by Thursday, on several technicalities of the commission, including allowing an inspector overseeing the commission to get forward notice of impending public hearings.

One sticking point was the definition of corrupt conduct that could be referred to the commission, as the government wanted misconduct allegations to remain under the purview of the Public Sector Standards Commissioner.

But Mr Barr has agreed to a compromise position which would see serious misconduct able to be investigated, as well as serious and systemic corruption, under the definition defined in the Fair Work Act, rather than the wider definition used by the NSW Independent Commission Against Corruption the committee originally wanted.

Uniquely, Mr Barr pointed out the contrast between the debate over an integrity commission in the Assembly this week with the highly divisive debate on the same issues currently taking place in the Federal Parliament.

While ACT Labor, the ACT Greens and the Canberra Liberals variously took credit for the legislation now before the Assembly, the efforts of all parties have been crucial to developing one of the more complex pieces of law expected to be passed this year.

The original proposal was advanced by the Greens during the 2016 election campaign and swiftly endorsed by both major parties. Two separate but related committee inquiries have taken place, and both the opposition and the government put bills or detailed drafts before the committee for examination.

Despite the expected passage of the bill, all parties are expecting numerous amendments to the government's bill to be lodged by the opposition, and possibly the Greens, on specific details before the final bill passes.

Mr Barr also a introduced a second bill in the Assembly on Tuesday, specifically dealing with the coverage of ACT Policing.

That bill would essentially allow police coverage to be inserted into the main bill a year after the commission starts operating in July next year, partly to allow time for Mr Morrison and possibly federal Labor leader Bill Shorten to detail their positions.

It would also ensure that should a case come before the commission involving an ACT police officer before the Commonwealth passes changes to the territory's self-government act, it would prevent a potential appeal toppling the entire package of reforms.

Mr Morrison's office did not respond to questions about ACT police coverage on Tuesday, though he has previously referred to a federal anti-corruption commission as a fringe issue.