Support for Speaker Bronwyn Bishop is waning within the Liberals, but senior government members say an investigation into her expenses needs to finish before any action is taken.
The Finance Department is investigating all of Mrs Bishop's charter transport expense claims dating back to her 2013 elevation to Speaker, including a $5200 luxury helicopter taken on a 100km trip from Melbourne to Geelong for a party fundraiser last year.
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No confidence motion to be moved against Bronwyn Bishop
Mrs Bishop - who has agreed to pay back the money with a penalty - signed forms stating all of her charter trips were for "official business", but Labor says she should be sacked for misusing taxpayer money.
Foreign Minister Julie Bishop says the Speaker is considering her position as Labor will use the issue to "destabilise" the first parliamentary question time after the winter break on August 10.
"And I'm sure Speaker Bishop will take that into account as she considers her position," she said from New York.
"But I believe it's important the Department of Finance be able to carry out an investigation."
Social Services Minister Scott Morrison declined to say whether he had confidence in the Speaker.
"There is a Department of Finance process that's underway," he said on the Gold Coast.
"If I have anything to pass on to the Speaker I will do it privately and not offer public lectures on these things."
Communications Minister Malcolm Turnbull made light of the matter on Wednesday, by tweeting to his 396,000 followers as he took a tram and train from Melbourne to Geelong for a media event.
"Now on the 109 on Collins St to Sth Cross (sic) to get the train to Geelong to visit @SHendersonMP," Mr Turnbull tweeted, referring to Corangamite MP Sarah Henderson.
But Leader of the House Christopher Pyne threw his support behind Mrs Bishop as a "woman of resolve".
"I'm standing strongly behind Bronwyn Bishop as Speaker and I'd call on all my colleagues to stand firm against the demand from the Labor party to remove the speaker," he told Sky News.
Mrs Bishop is also facing questions over her use of taxpayer-funded expenses to attend the weddings of Liberal colleagues in 2006 and 2007.
The Speaker's office says on both occasions she had parliamentary business in areas near the weddings.
Prime Minister Tony Abbott paid back the money he claimed to attend the wedding of former Liberal MP Sophie Mirabella in Wangaratta.
Mrs Bishop claimed she had a meeting for a parliamentary committee in nearby Albury the day before the wedding.
But former Labor MP Jennie George, who was on the parliamentary committee, told Fairfax the committee had not authorised the work or received a report back.
Liberal frontbencher Jamie Briggs defended Mrs Bishop.
"You need in a national parliament for people to be moving around the country explaining what we're doing," he said.
A spokesman for Mrs Bishop said she would not be stepping down.
Opposition Leader Bill Shorten says Mr Abbott has to sack Mrs Bishop and replace her with respected veteran Queensland Nationals MP Bruce Scott.
Labor is expected to move a motion of no confidence in the Speaker if no action is taken before parliament resumes, as will two lower house MPs, Clive Palmer and Andrew Wilkie.
A spokeswoman for the Finance Department told AAP the department did not comment on its dealings with individual parliamentarians.
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