Liberal MP Julia Banks has announced she will quit Parliament at the next election, citing bullying and intimidation and the leadership crisis that engulfed the party last week as the "last straw".

Ms Banks, who holds the marginal seat of Chisholm in Victoria, said she had received hundreds of emails from constituents who wanted Malcolm Turnbull to remain prime minister and Julie Bishop to continue as deputy party leader.

"I have always listened to the people who elected me and put Australia's national interest before internal political games, factional party figures, self-proclaimed power-brokers and certain media personalities who bear vindictive, mean-spirited grudges intent on settling their personal scores," Ms Banks said in a statement.

"Last week's events were the last straw."

Scott Morrison took over as Prime Minister on Friday after a bruising leadership brawl.

Ms Banks said she felt compelled to call out bad behaviour within the Liberal Party, and would not tolerate bullying or intimidation.

"I have experienced this both from within my party and from the Labor Party," she said on Wednesday.

"The scourge of cultural and gender bias, bullying and intimidation continues against women in politics, the media, and across business."

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Concerned for welfare

Prime Minister Scott Morrison promised to stamp out bullying in the party.

"I will continue to consult with my colleagues about ensuring that there can be no question about the culture of the Liberal Party," Mr Morrison told reporters in Sydney.

"There should not be, and certainly under my authority, there would have been absolutely nothing of that sort taking place."

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Mr Morrison said he supported Ms Banks decision to take some time off after last week's "torrid affair".

"My first concern is for her welfare and wellbeing and she is taking the time to ensure that that's taken care of and she has my support fully in that."

Senior minister Mathias Cormann said any potential bullying investigation was a matter for the Liberal Party organisation.

"I've got very high regard for Julia Banks. I'm obviously disappointed that she's made that decision but I respect the decision," he told reporters in Perth.

Senator Cormann said he always treated colleagues with respect and would not condone anyone doing otherwise.

'Women have suffered in silence too long'

Ms Banks vowed to continue fighting for gender equality, launching a pre-emptive strike on any criticism she was playing the gender card.

"Women have suffered in silence for too long and in the last twelve months, the world has seen many courageous women speak out," she said.

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Ms Banks said she will take a few days leave before parliament resumes on September 10, citing the enormous emotional toll the political upheaval had taken on her.

The first-term MP holds the marginal seat of Chisholm by just 1.24 per cent.

Former minister Craig Laundy is also weighing up whether to leave politics after the bitter fallout from the tumultuous week of leadership tensions.

Mr Turnbull will resign his Sydney seat of Wentworth on Friday, triggering an October by-election.