Labor continues to pursue the government over the Jamie Briggs affair, calling on the federal police to investigate the leaked photo of the public servant who complained about the former minister.
Prime minister Malcolm Turnbull has all but ruled out an investigation, even though he said Mr Briggs shouldn't have shared the photo of the female public servant which ended up in the media.
But shadow attorney-general Mark Dreyfus says the "federal police or some other appropriate agency" should be called in to look into the matter.
Mr Dreyfus linked the Briggs affair to the government's delay in appointing a full time Sex Discrimination Commissioner, four months after Elizabeth Broderick left the post.
Human Rights Commission president Gillian Triggs has been acting in the role, while Attorney-General George Brandis told parliament in November an "announcement will be made very soon".
Mr Dreyfus said it's unacceptable women suffering discrimination have been left with no dedicated advocate for four months.
"I'm floored that the government doesn't seem to care that Australia has no Sex Discrimination Commissioner," he told ABC radio on Wednesday.
The Greens have also called on Mr Turnbull to sack immigration minister Peter Dutton who labelled News Corp journalist Samantha Maiden a "mad f***ing witch" over a column she wrote criticising Mr Briggs.
The prime minister has described Mr Dutton's text, which he accidentally sent to Ms Maiden instead of Mr Briggs, as clearly inappropriate.
But Greens leader Richard di Natale said Mr Dutton should be replaced by a "capable woman".
"There's no question there is a boy's club in Canberra," Senator Di Natale told reporters in Melbourne.
The actions of Mr Briggs and Mr Dutton have dominated the start of an election year for the coalition.
Mr Turnbull's predecessor on Wednesday urged him to keep his promise of holding the poll toward the end of the year.
Tony Abbott made the comment while renewing his push for a registered organisations commission and the re-establishment of the construction watchdog, following royal commission findings into trade unions.
"Swift passage of the `clean unions' legislation should mean an election at the usual time towards the end of the year as the prime minister has promised," he wrote in The Australian.
