The Opposition has ramped up its pressure on Michaelia Cash, calling for the outspoken employment minister to resign over an outburst in Senate Estimates on Wednesday.
Senator Cash was facing questions over the actions of her staff, one of whom resigned last year after it was revealed they tipped off television networks so they could film a police raid on the offices of the Australian Workers' Union.
The senator responded by threatening to "sit here and name every young woman in Mr Shorten's office, over which rumours abound".
Labor senator Penny Wong later demanded she retract the "disgraceful and sexist" remarks.
Senator Cash did withdraw the comments, but has not apologised.
"If anyone has been offended by my remarks, I withdraw," she told the Senate committee.
Labor's shadow employment minister Brendan O'Connor on Thursdy called for the Turnbull Government minister to resign.
"She must apologise without qualification and resign," Mr O'Connor said.
Labor is accusing the minister of raising the rumours to distract from the AWU police raids.
"She cannot remain as a minister because she has refused to explain the extent of the involvement of her office and herself in leaking information, which is an unlawful act, to the media, and for that reason she must resign," he said.
The comments have drawn a mixed reaction from the government's own benches.
Finance minister Mathias Cormann said the outraged response from Labor was because Senator Cash was a "very effective operator" who had taken effective action against union corruption.
Liberal MP Michael Sukkar said he could "understand her frustration" at political attacks on individual staff members.
But former prime minister Tony Abbott told 2GB the comments were a "brain snap" and a "cheap smear".
Education minister Simon Birmingham said he liked politics to be conducted "as respectfully as possible".
"I think Michaelia acknowledged in Estimates yesterday that perhaps a line had been crossed, which is why she withdrew the remarks," Mr Birmingham said.
