“She’s completely lost if she doesn’t think she needs to acknowledge that there’s something wrong with cheating kids and community sports clubs … I just think it’s disgusting,” Ms Steggall told ABC radio on Friday.
Senator McKenzie is refusing to apologise, insisting no rules were broken.
Ms Steggall took aim at Scott Morrison and compared him to former Australian cricket captain Steve Smith, who served a one-year ban for failing to stop cheating within his team.
“We saw the outcry with the cricketers, and they took responsibility, they acknowledged where they had gone wrong and where their standards had slipped,” Ms Steggall said.
“The standards of the members of your team, they’re a direct reflection on the standards of you as a captain. It’s just quite concerning that is what they think is acceptable conduct.
“We really need a national integrity commission, there needs to be some accountability. How low are you prepared to let the standard drop.”
Senator McKenzie found support from frontbench colleague Peter Dutton who said she shouldn’t have to resign.
“None of those clubs that received that money have been found ineligible,” Mr Dutton told the Nine Network.
“I’ve been in the parliament a little while, I can remember the years in opposition where the Labor minister, the Labor candidate, the Labor senator, would come out and make announcements for funding in your local community.
“This isn’t anything new in that sense. Now we’ll have a look at the auditor-general’s report, obviously, but none of those clubs, very deserving sporting clubs, have been found ineligible.
“The money has gone out – not against recommendations, not to clubs that weren’t deserving of it – but to clubs that are trying to get small kids in.”
Opposition Leader Anthony Albanese said Senator McKenzie’s position as minister is “untenable”.
“She made political decisions based upon the marginality of electorates,” he told reporters in Melbourne.
Independent Tasmanian senator Jacqui Lambie backed calls for Senator McKenzie to resign, and promised to support a parliamentary inquiry, which the Greens will also support.
“I agree with Zali Steggall it is disgusting and where is our PM on this? Are there any consequences for this shocking behaviour?” Senator Lambie tweeted.
Federal Bureau Chief Canberra