The former Border Force chief Roman Quaedvlieg has provided a new submission to the Senate over the Peter Dutton au pair saga and doubled down on claims that he was asked to help a “mate” of the minister who had a visa problem.

After a day of claim and counter-claim on Thursday, Quaedvlieg gave a supplementary submission on Friday to the Senate inquiry investigating the au pair issue.

The inquiry is examining allegations Dutton used his ministerial powers to overrule his own department and grant visas to at least two au pairs.

The committee secretariat has not made the new submission by Quaedvlieg public.

Quaedvlieg claimed in his earlier submission that he was called by Dutton’s chief of staff in June 2015 asking about the detention of a prospective au pair for the “boss’s mate in Brisbane”. After Quaedvlieg provided details of the case, he says he was asked: “What needs to be done to fix this? Can the boss overturn it?”

Dutton forcefully rejected the version of events set out in Quaedvlieg’s first submission on Thursday, calling them false and fabricated.

The home affairs minister said he never ordered any staff member to make this phone call, and that the conversation could never have happened because his chief of staff, Craig Maclachlan, did not work for him in June 2015.

However, documents uncovered from within the Department of Prime Minister and Cabinet from April 2015 show Maclachlan was working in the office of the then prime minister, Tony Abbott, before moving to Dutton’s in October.

Quaedvlieg says he is “adamantine” the phone call occurred but that the case might not relate to one of the two au pair cases already revealed before the Senate, but to yet another one.

Quaedvlieg’s intervention is further evidence of a falling out between him and the minister he once worked for, as well as with the home affairs secretary, Mike Pezzullo.

Quaedvlieg was sacked as ABF commissioner in March for allegedly helping his partner get a job at Sydney airport, allegations he denies. Quaedvlieg remains under investigation.

He declined to comment on his second submission “other than to state unequivocally that the effective substance of my original submission stands”.

One of the au pairs, detained in Adelaide on suspicion she was going to work in breach of her tourist visa, was French woman Alexandra Deuwel, who was on her way to work for Callum MacLachlan.

Maclachlan contacted his second cousin, AFL chief Gillon McLachlan, seeking help to have Deuwel released.

Gillon McLachlan told the inquiry this week that he instructed his government relations officer Jude Donnelly, another former Abbott staffer, to contact Dutton’s office.

The other au pair was an Italian woman Michela Marchisio, detained in Brisbane, who was going to stay in the home of Queensland police officer Russell Keag. Dutton worked with Keag in the Queensland police force in the 1990s but has said publicly he had not spoken to him in 20 years.

Meanwhile, with parliament set to resume on Monday, the Greens MP Adam Bandt has written to the prime minister, Scott Morrison, saying Dutton misled parliament over his role in the au pair visa grants and must be sacked from cabinet.

On 27 March this year, Bandt asked Dutton during question time if he could “categorically rule out any personal connection or any other relationship between you and the intended employer of either of the au pairs”.

Dutton told the house: “The answer is yes. I haven’t received any personal benefit. I don’t know these people.”

It has since emerged that Dutton did know Keag, and that the pair served in the police force together for about two years, according to Dutton.

Bandt wrote to Morrison: “The minister has publicly admitted he had a personal connection with the person in question, contrary to what he told the House. I have publicly invited the minister to fully explain the inconsistency between his answer to the House and his public statements, but he has instead reaffirmed that he stands by his answer to the House ‘100 per cent’.”

Bandt said Dutton had breached the government’s own statement of ministerial standards, which requires ministers to “provide an honest and comprehensive account of their exercise of public office”.

“Accordingly, I request that you immediately dismiss Mr Dutton from his ministerial portfolio and your cabinet. Failure to do so will make it clear that ministers can mislead members of parliament with impunity and that the rules you set for your ministers aren’t worth the paper they are written on.”

Dutton has consistently defended his actions, saying: “I make decisions on the merit of individual cases according to the law.”

Morrison has thrown his support behind Dutton.

“I believe he has the confidence of the Australian people, and certainly of his team, to ensure that we keep our borders secure,” he said.

