The secretary of the Department of Prime Minister and Cabinet, Martin Parkinson, is usually responsible for investigating alleged breaches of the ministerial code.
However Mr Turnbull said enforcement of the sex standard would “rely on the integrity and commitment of ministers”.
Labor has refused to commit to retaining the new standard should it win power, and accused Mr Turnbull of using it to distract from his failure to act against Mr Joyce.
Deputy Labor leader Tanya Plibersek on Friday suggested the change was unnecessary.
“Does anybody genuinely believe that writing a clause into the Prime Minister’s code of conduct – which the Prime Minister has shown he’s completely unable to enforce already – is going to make a difference to people’s behaviour in private?” she said.
“Honestly, are we really the country that starts sticking long lens cameras in people’s bedrooms?”
Members of the government have also previously expressed scepticism about bans on sex between politicians and staff, after the US House of Representatives this month voted for such a measure.
Foreign Minister Julie Bishop told the ABC that the government “has no business interfering into people's personal lives and we wouldn't want to cross the line, so moral police were able to dictate what happens between consenting adults”.
Labor says Mr Turnbull has failed to enforce what they say are Mr Joyce’s breaches of the existing code of conduct, including when, after his marriage breakdown, he accepted free rent from a friend whose business has received taxpayer funding.
Mr Turnbull has signalled further changes to the code, which he described as a “rather old document”.
Many outstanding questions remain over the sex ban, including what behaviour constitutes “sexual relations”.
Finance Minister Mathias Cormann would not elaborate on Friday, telling Sky News: “I’m not going to get into the weeds of all of this ... I think that people know what conduct is inappropriate”.
Sex Discrimination Commissioner Kate Jenkins said while leaders should set the tone in workplaces about appropriate behaviour, she did not think “a blanket ban is necessary in all cases”.
“There is not a one-size-fits-all solution because not all workplaces are the same,” she said.
Ms Jenkins said all employers should have a sexual harassment policy.
“I think this issue is distracting us from the broader concerns around gender equality and sexual harassment in the workplace, and I would hate to see further barriers created for women to progress their careers,” she said.
Nicole Hasham is environment and immigration correspondent for The Age, The Sydney Morning Herald, Brisbane Times and WAtoday.
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