Federal government MP Andrew Broad says he footed the bill for an international trip to Hong Kong during which he had dinner with a younger woman he met online.
But Mr Broad has said he would be willing to repay some domestic transport costs between his northern Victorian electorate and Melbourne if required.
The Nationals MP resigned as assistant minister to Deputy Prime Minister Michael McCormack on Monday, after New Idea magazine published an article about the alleged details of the meeting.
A woman, named as "Amy", claimed she met the married 43-year-old in Hong Kong in November for dinner and he told her he was there for a "conference" but "shouldn't have been here at all".
The woman also claimed the Mr Broad lied about his age, sent her numerous text messages that turned to a "more sexual nature" following the dinner and compared himself to "James Bond".
The MP for the northern Victoria seat of Mallee has now told The New Daily he was in Hong Kong in for a fruit and vegetable trade show, linked to his electoral work, in early September rather than November as the New Idea story suggested.
He told the news website he had "paid for it all myself" but could repay a domestic part of his journey should that be required.
"All international travel was self-funded, and any travel domestically between Melbourne and Mildura can be repaid if needed," he said.
Mr Broad's parliamentary expenses record shows he travelled from Mildura to Melbourne on September 2 and from Melbourne to Mildura on September 7.
Mr Broad said he was not one to "put myself on a moral high ground" because he made "mistakes" like anyone else.
"Government is imperfect people governing imperfect people," he said.
Mr McCormack told reporters on Monday he had known about the matter for a couple of weeks and had urged Mr Broad to report it to the Australian Federal Police.
But the AFP said in a statement on Monday it had received Mr Broad's referral on November 8, six weeks earlier.
After assessing it, the AFP found "no applicable offences under Australian law".
In a follow-up statement, the deputy prime minister said he had thought a couple of weeks ago was "approximately" the time of the call and had been told by Mr Broad his trip to Hong Kong was a personal one.
Meanwhile, The Herald-Sun on Tuesday cited unnamed "senior Nationals" saying they feared the allegations could be the "tip of the iceberg" for Mr Broad, claiming at least three women had contacted the party in the past year.
These women made separate claims of "dalliances" with Mr Broad, dating back to 2015, the news outlet reported.
It is the second sex scandal to rock the Nationals this year after a married Barnaby Joyce was forced to resign as party leader following revelations he was expecting a child with a former staffer.
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