Labor has referred Speaker Bronwyn Bishop to the Australian Federal Police over her chartered helicopter flight to a Liberal fundraiser.
Mrs Bishop has offered to pay back more than $5200, plus a 25 per cent loading, claimed for the 100km helicopter flight between Melbourne and the Clifton Springs Golf Club in Geelong for a Liberal party function last year.
Labor's waste watch spokesman Pat Conroy on Friday wrote to the AFP seeking an investigation into whether Mrs Bishop made a false statement when she signed a Finance Department form stating the charter was claimed for "official business".
Knowingly making a false statement is a criminal offence.
Labor frontbencher Tony Burke said he did not accept that an MP could get on a helicopter and "accidentally" attend a Liberal fundraiser.
"We're in a situation now where she will not answer a basic question, which is: has she or has she not lied on a form which, if you lie on, carries criminal penalties?" Mr Burke told reporters in Sydney.
"If there is a reasonable explanation, then Bronwyn Bishop should give it to the Australian people, and she should provide it to the Australian Federal Police."
Mrs Bishop's spokesman said on Thursday the Speaker stood by her assertion that the claim was made within the rules.
Mrs Bishop attended the event at the Clifton Springs Golf Club on November 5, just after the writ was issued for the Victorian state election.
Despite being scheduled to do so, the Speaker did not attend a ceremony in Canberra on Friday to remember the victims of the MH17 disaster.
Fairfax reported on Friday that a political lobbyist who is a friend of Mrs Bishop's chief of staff had arranged the helicopter charter.
Comment has been sought from the charter company Air Melbourne.
Greens senator Lee Rhiannon said there should be an independent investigation into the helicopter company's ties with the Speaker's office.
"The more details revealed about this absolutely extraordinary episode the more apparent it becomes that something fishy is going on," Senator Rhiannon said in a statement.
There should also be a broader review of entitlements rules, she said.
Independent senator Nick Xenophon said he would seek parliament's support for an independent entitlements umpire to which the public could take complaints.
Travel disclosures should be made within 30 days of the travel occurring, he said.
Opposition Leader Bill Shorten said in a statement on Friday that putting Mrs Bishop in the Speaker's chair was "one of Tony Abbott's most famous captain's calls".
"She was his personal choice and her conduct as Speaker is entirely his responsibility," Mr Shorten said.
"It's time for Tony Abbott to say if he continues to have confidence in Bronwyn Bishop as Speaker - this is a test of his leadership."
In 2012 as opposition leader Mr Abbott described then Speaker Peter Slipper as "the prime minister's creation", referring to Julia Gillard.
"This Speaker's standards are this prime minister's standards," Mr Abbott said at the time.
Liberal frontbencher Christopher Pyne questioned the timing of Labor's criticism.
"Awful on the day we remember the anniversary of the destruction of MH17 that Labor wants to play politics over the Speakership," Mr Pyne wrote on Twitter.
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