"We've all got a job to do to ensure we do everything we can to keep families together and we all have personal responsibilities in that regard,"Mr Morrison said.
Mr Morrison challenged Labor and the Greens to replicate the ministerial rule for their own frontbenchers.
Mr Tudge responded to theFour Corners report by expressing regret at the hurt he caused his family and Ms Miller,but he did not respond in detail to the bullying claims whenThe Sydney Morning Herald andThe Age sent him extracts from the formal complaint on Tuesday.
The minister's spokesman said Mr Tudge had only learned of the complaint from the media and was not aware of any previous complaint.
"As appropriate,the minister anticipates that the Department of Finance would conduct an independent inquiry into this matter,"the spokesman said.
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Ms Miller makes no allegations of sexual harassment against Mr Tudge in her statement. The relationship took place before February 2018,which meant it did not breach the code.
But it follows warnings from other women about a cultural problem within the Liberal Party that disempowers women and turns a blind eye to sexual harassment.
The Age andThe Sydney Morning Herald last year revealed the experience of other advisers who were subjected to harassment and later told they should"just go along with it"because speaking up would hurt their career prospects.
Former advisers have privately warned of similar problems within the Labor Party while former NSW Greens MP Jeremy Buckingham was accused in state Parliament in November 2018 of engaging in"sexual violence"against women. An investigation did not substantiate the allegations,and Mr Buckingham strenuously denied them. He quit the party the next month and lost his seat at last year's state election.
Ms Miller's statement,lodged with the Department of Finance last Thursday,alleges bullying behaviour at the same time she and Mr Tudge formed a relationship during an intense period of travel for work.
"This friendship led to a personal,intimate relationship which was consensual,"she says in the complaint.
"I want to make it clear I make no allegations of sexual harassment or unwanted attention from Alan."
But Ms Miller says Mr Tudge could be"charming and caring"on one day and"belittling and humiliating"on another,which meant she could not be sure"which Alan I would get"on any day.
At one point,she alleges,after a visit to Bundaberg in Queensland to launch a welfare program in September 2017,Mr Tudge subjected her to criticism and attack about her work in front of other passengers on a flight home.
"I ended up in tears on the plane,the person sitting next to me gave me a very awkward smile and tried to cheer me up. They had witnessed the whole thing and it was very humiliating,"she writes.
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"This type of behaviour regularly occurred and left me feeling very nervous,anxious and afraid of what would happen each day."
Ms Miller lodged the complaint to call for a better system to support government and Opposition advisers,who are hired under the Members of Parliament (Staff) Act,giving ministers the right to hire and fire without some of the safeguards for public servants.
"I want to highlight the unacceptable workplace behaviours,but I also want to highlight that the MOPS system that should have protected me did not,"she writes.
"The staff turnover is appalling and should be sending clear signs that MOPS Act employees need more support and mandatory training that makes it very clear that bullying and harassment will not be tolerated."
The complaint says that Mr Tudge was responsible for his"poor behaviour"as well as being a victim of the pressure that comes from his role,although this was"no excuse"for actions that harmed the mental health of others.
Ms Miller,who worked as an adviser for more than a decade,says the failures of the government system became apparent when she moved to the private sector in 2018 and saw the support and training offered on bullying and harassment.
"MOPS need to implement a better system because I feel that had I had the support I needed I would not have lost a career that I loved,"she writes.
"The impacts on my marriage and my family,as well as our financial situation,have been extensive and shattering.
"I am making this complaint in the hope that others don’t have to go through the same experience."
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