"We’ve received no complaints,"said the president of the Liberal Party’s Victorian division,Michael Kroger,but he said he would"absolutely"look into the matter if Ms Banks brought incidents to his attention.
One of Mr Dutton’s supporters,NSW MP Craig Kelly,told Sky News that MPs had to"roll with the punches"during a leadership spill.
But one of Mr Turnbull’s supporters said members of Mr Dutton's campaign had"hounded"MPs to sign the petition needed to trigger the Friday vote that removed Mr Turnbull and installed Mr Morrison.
Victorian MP Sarah Henderson,who backed Mr Turnbull,last weekrevealed Mr Dutton's supporters offered her a ministry to secure her vote. She rejected the offer and was named Assistant Minister for Social Services on Sunday.
Ms Henderson issued a statement on Wednesday night to praise Ms Banks and condemn bullying but she aimed her criticism at Labor,not Liberal colleagues.
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"Politics is a robust and stressful business,particularly when contesting or representing a marginal seat,"she said.
"I have experienced unfounded attacks,bullying and intimidation by the Labor Party since I first ran for Parliament in 2009."
Industrial Relations Minister Kelly O'Dwyer said bullying"in any workplace,whether on the shopfloor,or in our nation’s Parliament"was unacceptable.
Mr Morrison vowed to change the culture of the party after the"pretty torrid ordeal"of last week,citing his two daughters to make it clear he had no tolerance for bullying.
"I will continue to consult with my colleagues about ensuring that there can be no question about the culture of the Liberal Party,"he said.
The dispute over bullying highlights the bad blood within federal Liberals over the leadership spill.
The Liberal Party’s Victorian division is now considering a search for new candidates to defend the seat of Chisolm in suburban Melbourne,which Ms Banks holds by a margin of just 1.6 per cent.
"The people of Chisholm know that I say what I think,"Ms Banks said.
"They know that I will always call out bad behaviour and will not tolerate any form of bullying or intimidation. I have experienced this both from within my own party and from the Labor Party.
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"I will always stand for equality regardless of peoples’ heritage,sexuality or gender."
The announcement came after a frantic 24 hours of negotiation as Mr Morrison and the party’s senior Victorian cabinet minister,Treasurer Josh Frydenberg,urged Ms Banks to fight the next election for the good of the government.
Fairfax Media understands Ms Banks told the two leaders of her decision on Tuesday but could not be persuaded to stay because of her frustration at the way Mr Turnbull and the deputy leader,Julie Bishop,were toppled.
Ms Banks held out against pressure to back Mr Dutton and voted for Ms Bishop in the first round and Mr Morrison in the second round of the leadership ballot.
In a rebuke to the conservative powerbrokers who blocked the rise of Ms Bishop and brought on last week’s turmoil,Ms Banks said"I’m not done"in her statement on Wednesday morning.
"In anticipating my critics saying I’m ‘playing the gender card’ I say this. Women have suffered in silence for too long and in this last 12 months the world has seen many courageous women speak out."
Ms Banks was the only Liberal candidate to win a seat from Labor at the 2016 election,gaining Chisholm after former speaker and Labor MP Anna Burke retired.
She will return to Parliament when it resumes on September 10 to shore up the government’s numbers,at a time when Labor is ready to exploit the absence of Mr Turnbull from the lower house.