The Finance Department is now investigating all of Speaker Bronwyn Bishop's expense claims, but despite apologising, she won't step down from the role.
Speaker Bronwyn Bishop says she's sorry over the expenses scandal and will pay money back, but won't be quitting.
Her apology on Thursday came as two independent MPs flagged a no-confidence motion when parliament returns on August 10.
"I want to apologise to the Australian people for my error of judgment and to say sorry," a contrite Mrs Bishop told 2GB on Thursday.
"I feel I've let them down."
Clive Palmer told SBS that he would move a motion of no confidence against the Speaker if she refused to step down before parliament resumed.
The Palmer United Party leader also posted the below video on Facebook, with a caption citing the impending motion which will be seconded by Independent Andrew Wilkie.
Mr Palmer has also launched an online petition.
Opposition Leader Bill Shorten told AAP if Mrs Bishop was genuinely sorry she would not have waited nearly three weeks to say so.
"There's a difference between saying sorry because you mean it and saying sorry because you're about to get the sack," he said.
"She's only saying sorry to save her job."
Independent MP Clive Palmer has demanded Mrs Bishop's resignation regardless of the apology.
He has challenged Liberal MPs to cross the floor, insisting parliament cannot function with her still in the role.
Liberal Senator Zed Seselja said the Speaker had apologised and he would not be joining the witch hunt against her.
"I'm not sure what more she can do in those circumstances," he told Sky News.
Labor has yet to decide whether it will back the motion proposed by Mr Palmer and fellow independent Andrew Wilkie.
Mr Shorten says if the Speaker does not step down before parliament resumes, the Australian people could have "no confidence in what's happening in parliament".
"They hope that the whole thing will move on, but it's been lodged in the minds of the Australian people," he told ABC radio.
Former Labor Speaker Anna Burke said Mrs Bishop should at least stand aside, if not resign.
She accused her successor of bringing parliament into disrepute, saying her position had become untenable.
Mrs Bishop claimed taxpayer-funded expenses to attend the weddings of three Liberal figures - in 1999, 2006 and 2007.
She insists the claims were made within the rules, but other Liberal members, including Prime Minister Tony Abbott, have paid back their expenses claimed for weddings.
The Finance Department is now investigating Mrs Bishop's entire expense claim history, not just chartered transport that included a $5200 helicopter charter, which she has paid back.
"There are lots of grey areas and I think it would be helpful to have certainty," she said of the expanded investigation, which she had approved.
"I know that I've disappointed and let down the Australian people.
"I won't be resigning."
Labor waste watch spokesman Pat Conroy said there was no guarantee the Finance Department investigation would be impartial, because the department's secretary had publicly commented on the matter.
Secretary Jane Halton told a Women in Focus function in Canberra on July 15 the helicopter claim would not have been a story if it had involved a male MP.
A Labor referral to the Federal Police has been passed back to the department.
Mr Shorten later told reporters in Sydney that Mrs Bishop's position as Speaker was untenable despite her reluctant apology.
"They've been dragged kicking and screaming to a forced apology with no understanding or comprehension of what they've done wrong," he said.
Asked whether Labor would move a no-confidence motion against Mrs Bishop, Mr Shorten said the opposition did not have confidence in her as Speaker.
"I don't think anyone has confidence in Mrs Bishop as Speaker anymore," he said.
Later on Thursday Mrs Bishop addressed a function in the regional Victorian town of Sale, reiterating her apology.
"I should have said sorry earlier ... I'll be working very hard to make amends," she said.