The senator has denied she misled parliament on her knowledge of Ms Higgins' 2019 rape allegation before it was made public in 2021.
Fending off sustained opposition questioning, Senator Gallagher said she knew of the allegations in the week before they were made public, but she kept the information confidential.
"I was asked to keep it to myself and I did," she told parliament on Tuesday.
"I won't stand here and go through private conversations I had with a person at the centre of a very, very difficult time in her life, a person who has had her privacy breached in the most egregious way over the last two years.
"I don't intend to disclose further interactions between any people who come to me and ask to keep their confidence."
Ms Higgins said she was raped by fellow Liberal staffer Bruce Lehrmann in Parliament House in 2019, a claim he has always denied.
Mr Lehrmann's trial was derailed due to juror misconduct and prosecutors did not seek a retrial, citing concern for Ms Higgins' mental health.
Questions over her conduct were raised after leaked text messages between Ms Higgins and her partner David Sharaz emerged last week, suggesting the pair strategised with the then-opposition senator about how to break the story.
But Senator Gallagher said she had always conducted herself with high levels of integrity.
"I have at all times been guided by the bravery and courage of a young woman who chose to speak up about an alleged incident in her workplace," she said.
"I have always acted ethically and with basic human decency on all matters related to Ms Higgins and I will continue to do so."
The finance minister hit out at members of the coalition, saying they were yet to make a personal statement to the parliament on what they knew about the alleged rape.
She said the attacks made by coalition MPs following the leaked text messages being revealed could discourage women from coming forward.
"The events of the past week with the media coverage, the questions surrounding the publication of a young woman's personal phone records that had been provided for use in a court, splashed across TV and newspapers with opposition members giddy with the coverage, has done nothing but seriously damaged this confidence," she said.
The leaking of the text messages has been referred to the Australian Federal Police.
Senator Gallagher was concerned the incident could compel women to keep allegations of serious sexual or violent abuse silent "to suppress the trauma".
"Subjecting her to further commentary in a very distressing time for her, as minister for women, I don't think it's acceptable," she said.
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