The former head of the Australian border force said Peter Dutton's chief of staff contacted him in 2015 to transmit a request from a "friend" of the minister, requesting that an Italian au pair be saved from deportation.
Roman Quaedvlieg, who was fired from his powerful position earlier this year, made the accusations in a letter to Labor Senator Louise Pratt, president of an ongoing Senate investigation.
The statements raise new questions about whether the man who requested the intervention was a "friend" of Mr. Dutton.
The minister acknowledges that he knew the man when they worked together in the Queensland police, but said he had not spoken to him in 20 years.
The case concerns one of the two au pairs, the Minister of Internal Affairs, Peter Dutton, who was not deported in 2015.
The young Italian woman arrived in June of that year and her visa was canceled by border officials, who believed that she intended to work with a tourist visa, but that she was later saved from deportation by a ministerial intervention from Mr. Dutton.
The leaked emails have already revealed that the request came from Russell Keag, a former colleague of the minister.
The minister and the new government of Morrison have played down the link, while Labor and the Greens claim that Mr. Dutton cheated Parliament when he claimed to have no personal connection to the families in question.
The deputy of the Greens, Adam Bandt, has taken advantage of the report and the "huge" accusations.
"Dutton confused [parliament] and he must go, "he tweeted.
Shayne Neumann, Shandne's immigration minister, said the prime minister should ask Mr. Dutton to explain the link.
"Obviously, Peter Dutton knew what he was doing and Peter Dutton obviously still had a personal connection with the police officer he served with the Queensland Police," Neumann said.
On Thursday morning, before the reports of Mr. Quaedvlieg's letter appeared in the media, Mr. Dutton told Radio 2GB that there was a "former ABF senior officer who leaked this information".
He did not name the person he suspected was dripping.
"Good luck to him if that's what he wants to do, obviously he's very close to the Labor Party … all that will come out at some point," Dutton said.
Over the weekend, Prime Minister Scott Morrison defended his cabinet colleague.
"How many people did you work with 20 years ago?" Mr. Morrison asked the journalists.
Mr. Dutton's department previously spent $ 10,000 trying to avoid publishing documents about au pairs in a freedom of information dispute with a journalist.