Labor leader Anthony Albanese, independent MP Zali Steggall and One Nation leader Pauline Hanson have all called for Bridget McKenzie to resign over her role directing $100m of sports grants to help the Coalition win marginal seats.

The deputy Nationals leader and former sports minister is under growing pressure, with the Greens, Hanson and Centre Alliance offering to support a Senate inquiry into the community sport infrastructure grant program, subject of a scathing audit office report.

McKenzie has defended her conduct, refusing to apologise or resign, claiming all grants were within the rules and Labor seats benefited from her intervention which she suggested amounted to “reverse pork-barrelling”.

On Friday Guardian Australia revealed concerns about politicisation of the grants, including Labor MP Graham Perrett who was excluded from the announcement of a $135,000 grant to the Sunnybank Saints in favour of his Liberal opponent, despite Perrett helping local club win the funding.

The Australian Financial Review reported that the Mosman Rowing Club in Tony Abbott’s seat of Warringah – under threat from Steggall – received $500,000, the maximum allowable under the program.

Albanese said it was “extraordinary and unprecedented” that Liberal candidates, such as Georgina Downer in independent-held Mayo and Angela Owen in Perrett’s seat of Moreton, were given oversized cheques to present as if they were responsible for the grant while local MPs were cut out of announcements.

“This is just a disgrace,” he told reporters in Sydney. “What we have seen is a government that is arrogant, in the lead-up to the federal election, used taxpayers’ money as if it was Liberal and National Party funding.”

“The truth is that [McKenzie’s] position is untenable as a minister.”

Sports Australia’s recommendations were “ignored in favour of political decisions as if they were election commitments”, Albanese said. “But they weren’t even that – they were funding from decisions by a minister with no basis that ignored the advice that was given to her.”

Earlier, Hanson told ABC News the audit office report had proven the Coalition had used the program “for pork-barrelling as a slush fund”.

“I call for [McKenzie’s] resignation – that she should step down in any portfolio as minister.

“I don’t think she is up to doing the job. I stand by that. This is case in point … Australian people are sick and tired of pork barrelling by politicians and looking after their own nest egg.”

The Greens have already suggested they will support a Senate inquiry into the sports grant program, and Labor has vowed to force the government to reveal unsuccessful applicants and the list of recommended projects overturned by McKenzie.

Senator Rex Patrick said Centre Alliance’s preference would be for a federal independent commission against corruption to investigate but “in the absence of such a body we will support an inquiry with appropriate terms of reference”.

Asked if she would support a Senate inquiry, Hanson said “yes … if it’s going to prove they’ve used that money, taxpayers’ dollars, to feather their own nest and further themselves”.

Steggall told Radio National “the whole thing is quite disgusting” and McKenzie should resign.

“She’s completely lost if she doesn’t think she needs to acknowledge there’s something wrong with treating kids and community sports clubs [unfairly] … in favour of prioritising projects for her own personal gain or the gain of the Coalition.”

The program awarded a total of $100m to 684 projects across three rounds in the months before the election, out of a total of 2,056 proposals seeking more than $396.6m.

The auditor general, Grant Hehir, found the successful applications were “not those that had been assessed as the most meritorious in terms of the published program guidelines”.

He found that McKenzie’s office had run a “parallel” assessment process in deciding how to hand out the funds, with a focus on marginal electorates.

In the first round, 91 of the projects (41%) approved were not endorsed by the Sport Australia board. In the second round, 162 (70%) of the approved projects were not recommended, and in the final round 167 (73%) of the approved projects were not recommended.