The comments by Therese Rein and Lucy Turnbull came as Prime Minister Scott Morrison explained why a Liberal staffer who made vile comments about an MP was sacked, but a minister who called a staffer a "lying cow" is still in her job.

Ms Turnbull and Ms Rein have been advocating for laws to be passed ensuring witnesses who come forward with evidence to an inquiry led by Sex Discrimination Commissioner Kate Jenkins to be allowed confidentiality.

The laws were introduced to parliament late on Thursday after an agreement was reached between the government and Labor.

Ms Turnbull said it was important the inquiry hear from as many people as possible.

"Some of them may not want to disclose their identities to keep their own ordeals and experiences, even traumas, confidential," she told the ABC.

Ms Rein said Ms Jenkins needed "frank and fearless information" about what has been happening in Parliament House and the extent of it.

"(If the laws are passed) then I would call on any women and men who have been harassed, groped, raped or sexually assaulted in any way and then had their careers threatened afterwards if they were to report, to come forward and to give that information in fullness to the review," she said.

Ms Turnbull said she did not personally see any "direct harassing behaviour".

"But I did see a situation, a workplace, with a very imbalanced power structure and a very, very male-orientated culture ... plus a lot of young women."

Both women said the prime minister should act on the recommendations of Ms Jenkins' 932-page Respect at Work report received in January last year, which set out such things as an independent anti-sexual harassment authority and law amendments.

"Don't just get the report, sit on it, hope it goes away. Do something now," Ms Turnbull said.

Mr Morrison has also received proposals from Liberal colleagues for a summit of women's peak organisations and "gender impact statements" for all legislation.

Meanwhile, federal government adviser Andrew Hudgson lost his job after being accused of yelling a slur at Tasmanian Greens leader Cassy O'Connor in 2019, while he was working for the premier.

The Department of Premier and Cabinet investigated the incident and could not substantiate the claim.

Mr Hudgson was subsequently moved to the office of federal frontbencher Michael Sukkar.

Ms O'Connor raised the incident under parliamentary privilege in the Tasmanian parliament on Wednesday night.

Mr Hudgson was then asked to resign.

The prime minister was asked why Mr Hudgson lost his job, while Defence Minister Linda Reynolds remained in cabinet, despite making comments - for which she has apologised - about alleged rape survivor Brittany Higgins.

"The particularly vile language that was expressed by that staffer - not on one occasion, is my understanding - this only very recently came to our attention," he told reporters.

"We dealt with this over the last couple of days, as I think you'd expect us to."

The issue of sexual harassment has been at the forefront of politics for weeks, after Ms Higgins claimed she was raped by a fellow Liberal staffer in 2019.

She has recently made a formal statement to police but Ms Higgins said she initially felt pressured to choose between keeping her job or going to authorities.

Australian Associated Press