The task force, chaired by former public servant Kerri Hartland, met for the first time on Thursday, and will oversee the implementation of all 28 recommendations from the Jenkins review.
The review was set up last year in the wake of allegations former Liberal staffer Brittany Higgins was raped in a ministerial office in 2019.
The review found one-in-three people working in Parliament House had been sexually harassed, with 11 per cent reporting it.
About one quarter of workers told the review their harasser was a politician.
Sex Discrimination Commissioner Kate Jenkins made 28 recommendations in the review, among them calls for gender diversity within parliament and setting up an independent complaints body.
The task force - made up of government, Labor and crossbench MPs - discussed delivering a statement of acknowledgement of the harms that have been caused in the parliamentary workplace.
However, it is not known when such a statement would be made.
The government indicated it would introduce changes to parliament when it reconvenes next week confirming fair work, along with age discrimination and disability discrimination laws, would now apply to the staff of MPs and senators.
The changes will also see work health and safety laws apply to MPs and senators in their role as an employer.
Finance Minister Simon Birmingham said the government had commissioned a review of the Members of Parliament Staff Act, which was one of the recommendations of the Jenkins review.
"The government has also already extended the funding for the parliamentary workplace support service so work can commence on its expansion," he said in a statement.
"It can continue to be made available to staff and parliamentarians, alongside extra funding for the parliamentary support line."
The review of the act will publicly report its conclusions by September this year, with submissions set to be opened shortly.
The task force discussed setting up a joint committee into parliamentary standards.
The committee would be able to look into and report on matters that related to developing codes of conduct for Commonwealth parliamentary workplaces.
The task force will meet regularly for the next two years while it oversees the implementations for the Jenkins review recommendations.
"The Jenkins report and its recommendations provide a roadmap to drive the cultural and practical change necessary to make our parliamentary workplaces safer," Senator Birmingham said.
"The government looks forward to continuing to work constructively with colleagues across the parliament to make the changes we need to ensure our workplace is safe, supportive and respectful."
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