Speaker Bronwyn Bishop is refusing to stand aside despite growing pressure over her chartering of a helicopter to attend a Liberal Party fundraiser.

Prime Minister Tony Abbott has also backed the speaker, insisting he won’t ask her to step down.

He says she’s admitted an “error of judgment” in chartering a $5227 helicopter ride from Melbourne to Geelong and had repaid the money.

• Bishop referred to federal police
• ‘Bronwyn Bishop should explain herself’: Hockey
• PM could pay price for Bishop

“She’s done the right thing, she’s a good speaker, she has my confidence,” he told reporters in Queensland on Saturday.

“I don’t think it’s appropriate for people to stand aside simply because the Finance Department might be having a look at something.”

Mrs Bishop described the allegations on Saturday as a “political beat up” and her office later told AAP she would not stand aside.

Tony Abbott said he will not ask Mrs Bishop to step down. Photo: AAP

She insists she made the booking and reported it in the ordinary way.

“When I saw the figure, it looked large and I thought I should pay it and I’m paying it,” she told reporters in Sydney.

Labor says Mrs Bishop should seriously consider resigning.

They’re demanding the Australian Federal Police investigate whether Mrs Bishop made a false statement when she signed a Finance Department form stating the charter was claimed for “official business”.

Opposition waste watch spokesman Pat Conroy wrote a second letter to the AFP on Saturday after they declined a request to investigate the matter on Friday.

An AFP spokeswoman said the matter would instead be investigated by the Finance Department under the Minchin Protocol, “the agreed protocol for dealing with matters of this nature”.

That’s despite the AFP having investigated former speaker Peter Slipper in 2012 over allegations he misused taxi dockets.

At the time, a Finance Department spokesman told AAP the Minchin Protocol did not apply where an allegation was referred directly to the AFP.

Mr Conroy says the AFP’s response is “inconsistent”.

“Is anyone seriously suggesting the Department of Finance should be investigating supposed criminal actions?” he told reporters in Newcastle.

“Is (Mrs Bishop) seriously claiming on that form that going to a Liberal fundraiser using $5000 of taxpayers money was part of being Speaker of the House of Representatives?”

Mr Conroy’s letter says the Minchin protocol is “no impediment” to a police investigation into Mrs Bishop’s conduct and is merely an administrative policy.

“This simple administrative policy cannot override the statutory obligation to investigate and prosecute crime which is imposed on the Australian Federal Police,” it says.

Mr Conroy demanded Mrs Bishop release the form she would’ve signed certifying the flight was for “official purposes” as speaker.

He said her position was becoming “increasingly untenable” and urged Mr Abbott to have a “hard conversation” with Mrs Bishop about her position.

Mrs Bishop later told reporters she would not resign although she had made an error of judgment and the amount paid for the helicopter was “clearly unacceptable”.

However that amount had now been repaid.

Asked if she would apologise she said: “the biggest apology one can make is to repay the amount,” she said.

“You don’t resign for an error of judgment if it’s within the guidelines,” Mrs Bishop said.

She said she had travelled by fixed-wing aircraft to two other speaking engagements in her time as speaker, and had asked the Finance Department to investigate her use of chartered flights on those occasions as well.