Former Liberal staffer Higgins alleges she was sexually assaulted by a fellow ministerial adviser in Reynolds’ office in 2019.

The minister on Friday apologised for last month calling her former employee a “lying cow” after being criticised for not offering enough support to Higgins at the time.

After lawyers fired off a letter threatening to sue Reynolds, she issued a fresh statement apologising for the remarks.

“Discussions are now under way through our legal representatives in an effort to resolve this matter as soon as possible, with any resolution to include an apology,” she said.

“However, in the meantime, I want to express how deeply sorry I am for these remarks and for any hurt and distress they have caused.”

Opposition leader Anthony Albanese is demanding the minister lose her job over the comment and handling of the rape complaint.

“What do you have to do to lose your job under Scott Morrison’s government? I find her position untenable,” he told reporters in Perth.

“The statement that she’s put out, it doesn’t cut the mustard.”

Prime Minister Scott Morrison said the minister retained his confidence to return to the job after her medical leave.

“This was a comment made not in a public place. This was a comment made during a period which was very traumatic and very stressful,” he told reporters in Sydney.

“The minister deeply regrets saying these things and has offered an apology, as she should.”

Higgins’ lawyers said the ex-staffer was appalled Reynolds apologised to staff who heard the remark but not her.

“Self-evidently, this demeaning and belittling statement, in which you refer to our client as a member of the animal kingdom and declare her to be untruthful, is highly defamatory of our client’s good character and unblemished reputation,” the letter said.

Government upper house leader Simon Birmingham said Reynolds needed to apologise to Higgins’ satisfaction.

Home Affairs Minister Peter Dutton said his cabinet colleague wasn’t questioning the veracity of the rape allegations, but responding to suggestions she hadn’t offered enough support.

“Linda genuinely felt hurt by the fact she thought she had provided every assistance possible obviously over a period of time,” he told the Nine Network on Friday.

Dutton said the prime minister was right to rebuke the defence minister but she did not need to resign.

Independent senator Jacqui Lambie said the leaks from Reynolds’ office showed the minister must relinquish the defence portfolio.

“When you’ve lost the respect of your own people and they’re going out to the media, I think you’re gone,” she told ABC radio.

Reynolds is on leave after her cardiologist recommended time off when she was under immense pressure over her handling of Higgins’ complaint.

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