Peter Dutton’s decisions to grant tourist visas to foreign au pairs in breach of work conditions were “anything but routine”, Labor has said, staring down Dutton’s warnings he will reveal representations made by parliamentarians on immigration matters.

Meanwhile, the Greens’ proposal for a no-confidence motion in the home affairs minister is gathering steam, with Labor offering support and Centre Alliance MP Rebekha Sharkie warning it “does appear” that Dutton mislead parliament when he suggested he had no “personal connection” to the employers of the au pairs.

Sharkie told Guardian Australia that Dutton’s answer to parliament was “quite concerning given what we now know” that representations were made on the au pairs’ behalf by a former colleague of Dutton’s in the Queensland police force and the Australian Football League chief executive, Gillon McLachlan.

“[Dutton] was emphatic in his response that he had no connection with them, that he didn’t know them personally,” she said. “I think you could argue that perhaps it was incorrect.”

The no-confidence motion is supported by Labor, the Greens and independent Andrew Wilkie but is still a few votes short despite the vacancy in the seat of Wentworth created by Malcolm Turnbull’s resignation.

The Nationals MP Kevin Hogan – who joined the crossbench in protest at the Liberal leadership change – said he would not support motions of no-confidence in the government, “including ministers”, ruling out joining the push against Dutton.

Sharkie said she would consult her Senate colleagues before deciding her vote on the motion, but called on the prime minister, Scott Morrison, to force Dutton to make a personal explanation of the answer and release correspondence to show what lobbying occurred before he made the decisions.

Sharkie noted the quick turnaround on the au pair cases, compared with “a couple of months to get a positive outcome” when the member for Mayo had approached Dutton on behalf of her constituents.

Under sustained pressure over the use of ministerial powers in 2015, when he approved visitor visas to an Italian and a French au pair facing deportation, Dutton on Monday said he did not mislead the parliament about the au pair controversy.

Dutton told reporters he answered the question in parliament in the context of suggestions his family benefited from the decision. “The allegation was that my family had – was going to – employ someone who was an au pair.”

On Tuesday Dutton confirmed he knew his former police colleague “from 20 years ago” but denied any personal motivation for intervening in the case.

“He didn’t have my mobile phone number, didn’t have my private email address,” he told Channel 7’s Sunrise.

“There’s no personal link there. I know him from 20 years ago. I’ve not socialised with him. I have no recollection of having even seen him in 20 years.”

Dutton has accused Labor and the Greens of “hypocrisy” for targeting him over the au pairs because MPs have regularly asked him to intervene in immigration cases, including the shadow treasurer and former immigration minister Chris Bowen.

He warned he has kept a list of Labor MPs who have approached him with “quirky” visa cases, adding on Tuesday that “there are links back to unions that have made donations to the Labor party”.

Bowen responded in a statement that “of course” he had made representations on behalf of constituents. “That is my job,” he said.

“I can confirm that at no stage have I made any representations on behalf of au pairs at airports who are pretty clearly in breach of the rules.

“And neither did I, during my three years as immigration minister, approve any.”

The manager of opposition business, Tony Burke – another former Labor immigration minister – said “of course” he had forwarded immigration cases to the minister for a decision.

“When I was minister did I intervene to help au pairs at airports who had broken the rules? Of course I didn’t.”

Shayne Neumann, the shadow minister for immigration, said that Dutton’s ministerial interventions to stop the au pairs from being deported “are anything but routine”.

Since becoming the immigration minister in December 2014, through to 30 June 2018, Dutton used his ministerial powers to intervene and grant visitor (subclass 600) visas only 14 times.

“Australians are right in asking why there are repeated instances of people with connections to Dutton getting visas for their au pairs – it stinks,” Neumann said.

“Peter Dutton can try to sling mud at others all he likes, but he can’t hide the fact that as the minister responsible, he had the decision-making authority in these cases and he needs to come clean.”

As well as the no-confidence motion in the House of Representatives, the Senate has initiated an inquiry into Dutton’s decisions.