Michaelia Cash's controversial comments about women who work in Parliament House have set off a new round of personal mudslinging, with fellow government minister Peter Dutton saying he won't tolerate a "morals lecture" from Labor figures who have a "history of problems" in their private lives.

Labor is demanding Senator Cash resign for her extraordinary outburst in Senate estimates on Wednesday when she threatened to "name every young woman" working in Opposition Leader Bill Shorten's office who is the subject of rumours.

Senator Cash made the comments during questioning about her staff in the wake of the scandal that rocked her office last year, when her media adviser quit after tipping off the media about a raid on the Australian Workers Union.

The opposition branded her comments "disgraceful and sexist" and demanded she withdraw. She offered a qualified withdrawal but did not apologise.