The former Liberal staffer reached a settlement with the Commonwealth in December 2022 after she launched legal action against her employers in the previous coalition government.
Ms Higgins alleged she was raped by Bruce Lehrmann in 2019 inside the ministerial office of then coalition minister Linda Reynolds, who they both worked for.
After the 2019 federal election, Ms Higgins worked as a media adviser for then-employment minister Michaelia Cash.
Mr Lehrmann has always denied Ms Higgins' allegation.
Media reports of text messages between Ms Higgins and her partner David Sharaz suggest the pair discussed potentially strategising with Finance Minister Katy Gallagher, when she was in opposition, after the rape allegation was made public.
Senator Reynolds indicated she could refer the compensation payment to the National Anti-Corruption Commission.
Prime Minister Anthony Albanese and Opposition Leader Peter Dutton both commented on the matter for the first time since Mr Lehrmann's high-profile criminal trial was abandoned because of juror misconduct.
Mr Albanese said he had "absolute confidence" in Senator Gallagher and rejected suggestions Ms Higgins and Mr Sharaz had used Labor MPs to publicise the allegation.
He said the first time he met Ms Higgins was on the public record at the time and happened on the same day she met with former prime minister Scott Morrison.
But Mr Dutton said the government had questions to answer and backed calls for the matter to be referred to the integrity commission.
"Linda Reynolds is a person of great honour and she feels rightly aggrieved in the process here," he said.
"I suspect this would be one of the first issues that the integrity commission would deal with.
"We're talking about multi-millions of dollars here, we're talking about senior ministers of the government potentially having conspired or at least having collaborated with individuals, and a lot of that needs to be explained."
Prosecutors ultimately dropped the charge against Mr Lehrmann because of fears about the impact of a second trial on Ms Higgins' mental health.
Attorney-General Mark Dreyfus, involved in the mediation process, said Ms Higgins' settlement was entirely in accordance with the law.
"It's very common for the Commonwealth to settle claims on the basis of agreed confidentiality," he said.
"It's very often in the Commonwealth's interests that there be confidentiality and, often in the case of sexual harassment claims, there is a desire on the part of the claimant to keep the matter confidential."
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
Lifeline 13 11 14
beyondblue 1300 22 4636
12°C