Senator Cash backed down from the threat on Wednesday after the opposition pressured her to withdraw the "disgraceful" outburst made during a parliamentary inquiry.

The jobs minister reacted angrily when Labor frontbencher Doug Cameron asked if her newly appointed chief-of-staff, who is yet to start work, was formerly employed in another Liberal office.

"If you want to start discussing staff matters be very, very careful because I'm happy to sit here and name every young woman in Mr Shorten's office over which rumours in this place abound," Senator Cash told the Senate hearing under parliamentary privilege on Wednesday.

"Do you want to start naming them? Do you want [me] to start naming them for Mr Shorten to deny any of the rumours that have been circulating in this building now for many, many years?"

Deputy Labor leader Tanya Plibersek called on Prime Minister Malcolm Turnbull to ask the WA senator for a proper apology, rather than her "mealy-mouthed weasel" retraction.

"Senator Cash's comments where ghastly, they were sexist, they were a 1950s style throwback," Ms Plibersek told parliament.

Labor's Senate leader Penny Wong earlier told the Senate hearing the minister had made "outrageous slurs" against female staff working in the opposition leader's office.

"It can't be allowed to stand. I think it is disgraceful and sexist and it is impugning of the character of various staff. I would ask the minister to withdraw," Senator Wong said.

Senator Cash disagreed with Senator Wong, arguing she was responding to Senator Cameron maligning her staff.

"The point I was making was rumours circulate in this building - it does not mean they are true," Senator Cash said.

After being asked to withdraw a second time, Senator Cash said: "If anyone has been offended by my remarks, I withdraw".

Liberals were at odds over the comments, with former prime minister Tony Abbott calling them a "brain snap" and junior minister Michael Sukkar saying they were "probably justified".

Mr Abbott called for the "cheap smear" to end.

"It is bad when it comes from the Labor Party, it is bad when it comes from the Liberal Party and it is particularly bad when it comes from a minister of the crown," he told 2GB.

The initial threat came after Senator Cash angrily brushed off demands to name her new chief-of-staff, saying it would break with convention.

"If you want to play that game, it is a very dangerous game to play," she said.

The Community and Public Sector Union demanded Senator Cash's resignation.

"How much baseless and hurtful speculation will young women working in parliament now endure because of the senator's ill-judged outburst?" CPSU national secretary Nadine Flood said.

Labor has been pursuing Senator Cash over raids at Australian Workers Union offices last October.

Details of the police raids were leaked to media by one of her advisers, who later quit.

Australian Associated Press