The party room will decide the next Speaker of the Parliament, Prime Minister Tony Abbott says, signalling he will not repeat the so-called "captain's pick" that led to Bronwyn Bishop taking the coveted chair.
The pledge comes as MPs jostle to replace Mrs Bishop in the plum role.
Labor has demanded her successor restore balance to parliamentary debate and not be drawn from the government's ranks of "fierce right-wing political extremists".
Mr Abbott has come under fire for indicating on Sunday that Mrs Bishop's downfall was primarily due to a flawed parliamentary entitlements system, playing down her misjudgment in claiming controversial expenses, including a private $5000 helicopter ride from Melbourne to Geelong.
On Monday Communications Minister Malcolm Turnbull deviated from Mr Abbott's defence of the Liberal stalwart, saying "common sense", rather than technicalities, should be the guiding principle when MPs claim travel expenses.
Mr Abbott had been under increasing pressure to orchestrate Mrs Bishop's resignation, as the scandal dominated the political agenda and effectively paralysed the government.
A prime minister does not have the power to single-handedly remove a Speaker. However, Mr Abbott is believed to have handpicked her for the role and the scandal was reflecting poorly on his leadership.
On Monday Mr Abbott said Mrs Bishop had vacated the Speakership of her own volition.
"Yes, there had been a number of conversations that I'd had with her over previous days and weeks, but she did the right thing unprompted after having done the wrong thing before," he said, adding a new Speaker should be swiftly chosen.
He said the selection of a Speaker was "always a matter for the party room".
"Sometimes there's only one nomination," he said. "There was only one nomination just after the [2013] election, but it's always a matter for the party room."
He rejected suggestions Mrs Bishop had been offered a job, now or in the future, in exchange for stepping down.
Mr Abbott predicted "quite a number of good people" would put their hands up for the Speaker's job.
"Whether there's a range of candidates offering themselves to the party room, whether a consensus develops behind a particular candidate, that's a matter that will unfold in the next few days," he said.
The Speaker sets the tone of debate in the chamber and must have a good knowledge of parliamentary procedure. Ideally, they would also be respected by MPs across the political spectrum.
Names being tossed around include Nationals MP and Deputy Speaker Bruce Scott, the longest serving lower house MP Philip Ruddock, moderate Victorian Liberal Russell Broadbent, and Liberal MPs Jane Prentice and Sharman Stone.
Ms Prentice is on the "Speaker's panel" - a group of MPs who can be called on to take the chair as needed. Dr Stone is a respected, outspoken parliamentary veteran.
In a statement, Mr Ruddock said he would step into the Speaker's role "if my parliamentary colleagues sought it".
Mr Ruddock has been a close ally of Mr Abbott but was dumped as chief whip in February after suggestions he did not adequately protect the Prime Minister from a spill attempt.
Mr Scott will assume the role of acting Speaker after Mrs Bishop's resignation. On Monday a spokeswoman for Mr Scott said he did not wish to comment on speculation he may permanently take the chair.
Should either Dr Stone or Ms Prentice take the role, it would help address the dearth of female government MPs in senior roles.
Dr Stone told the ABC on Monday she would "have to think very very seriously about it. I actually do think it shouldn't be a matter of the job being offered; it should be a matter of the party room voting [for the Speaker]."
The office of Ms Prentice declined to comment.
On Monday ABC News Breakfast host Virginia Tripoli tweeted that Mr Broadbent had told her "it's possible" he had Mr Abbott's support to take the Speaker's role. A spokesman for Mr Broadbent would not confirm the exchange.
Speaking on 2UE on Monday, Education Minister Christopher Pyne said while Mr Ruddock would make a good Speaker, "there will be quite a few people who will offer themselves up for the speakership; it's very early days".
"People are thinking about it this morning as they were last night. My phone has been running hot, as you can imagine, with people who want to talk about it," Mr Pyne said, agreeing with suggestions that "a Melbourne Cup field" of contenders would emerge.
Social Services Minister Scott Morrison told 2GB there were many good contenders when asked about Mr Ruddock's chances of being named Speaker.
"I think there are a lot of good candidates and I think it's important that the Parliament now do its job and … work through those processes," he said.
"Obviously, Philip, as the father or the house, has enormous respect, particularly his achievements as a minister were outstanding.
"But there are many others and I think it's important for the party to go through that sort of grass roots process within our own ranks, of our own party room, to move forward with a new Speaker."
Opposition Leader Bill Shorten on Monday threw his support behind Mr Scott, who has announced he will not recontest his rural Queensland seat of Maranoa at the next election.
Mr Shorten said Mr Scott was "sufficiently unpartisan; he's unrancorous". He accused Mrs Bishop of presiding over "appalling displays" while in the Speaker's chair, including ejecting almost 400 Labor MPs from the chamber.
"Speaker Bishop, the captain's pick of Tony Abbott, [was] running the equivalent of a parliamentary protection racket for the last 21 months ... turning question time into a complete joke," he said.
"I do think we need a more independent Speaker."
Mr Shorten also indicated support for Dr Stone.
Mr Abbott has announced a broad review of the entitlements system.
On Monday he said it would lead to root-and-branch reform that ensured "members of Parliament are working for the Australian people and not simply off on frolics of their own".
