The Morrison government has missed its own deadline to release its integrity commission legislation for consultation, with Christian Porter refusing to commit to a timeline for its passage.

The independent crossbencher Zali Steggall said the McKenzie sports grant revelations were further proof of the “urgent need” for a federal body capable of investigating the actions of commonwealth MPs and ministers.

However, the attorney general held firm to the need for “extensive consultation”, declaring it will “take as long as necessary”, dashing hopes the Morrison government will move quickly to establish the body, despite Porter’s promise to release the draft bill before the end of last year.

Porter admitted the government had missed its self-imposed deadline, as it faces a fight winning over members of its own backbench who remain concerned the two-tier proposal won’t hold ministers and MPs to account.

“Work to deliver the commonwealth integrity commission draft consultation bill is now all but complete,” Porter told the Guardian.

“But rather than starting the consultation process during the holiday period, which is not an ideal time to start a process of public scrutiny, I have decided to release the full 300-plus pages of the draft early in the new year.

“The consultation process will be extensive and will take as long as necessary to ensure the model we deliver has the powers and resources it needs to be effective, while also avoiding the pitfalls that have been seen with similar state-based bodies.”

The scathing auditor general report into former sports minister Bridget McKenzie’s handling of Sports Australia grants has reignited debate over the need for a federal integrity body, capable of investigating MPs.

“We are seeing numerous examples of ministers and their staff acting unscrupulously with no clear consequences – not only with the former sports minister Bridget McKenzie overriding Sport Australia’s grant recommendations, but also with minister Angus Taylor whose office has allegedly fraudulently amended a City of Sydney document to discredit an elected official,” Steggall said.

“Politicians are elected to represent Australians and should do so with honesty and integrity. But this is not happening and the bar needs to be raised. Behaviour such as that of Senator Bridget McKenzie brings the Australian parliament and the Australian government into disrepute.”

Labor has vowed to establish a Senate inquiry into the grants, which Jacqui Lambie has already pledged support for.

I agree with Zali Stegall it is disgusting and where is our PM on this? Are there any consequences for this shocking behaviour? Bridget Mcakenzie should resign now & I will be supporting a senate Inquiry #auspol #nationalICAC https://t.co/XUpsreNNNJ — Jacqui Lambie (@JacquiLambie) January 16, 2020

The Auditor’s report raises some serious questions that require examination. @centre_alliance’s preference would be that this matter be referred to a Federal ICAC for investigation, but in the absence of such a body we will support an inquiry with appropriate terms of reference https://t.co/Dr9H05BLoD — Rex Patrick (@Senator_Patrick) January 17, 2020

This minister has absolutely no shame. This is why we need a powerful and independent National Integrity Commission now, and why Mr Morrison and Mr

Porter refuse to establish one. https://t.co/Pbjj2wiEbo — Mark Dreyfus (@markdreyfusQCMP) January 16, 2020

The Senate has limited powers to force a MP into acting, and can only make recommendations. McKenzie has said she sees no reason to step down over the handling of the grants, calling it “reverse pork barrelling” when questioned over its legitimacy.

Taylor has also dug in against calls for his resignation from the front bench, over the doctored document affair, repeatedly insisting that neither he, nor any member of his office, altered the document in question. Taylor has claimed the figures used in an attempt to shame Moore and the city of Sydney council over its extensive air travel came from the council’s own annual report. Metadata shows the council’s publicly available report on its website was not altered after it was first uploaded in November 2018.

The AFP is still considering a referral from the New South Wales police to investigate the matter.