Senator Reynolds faced repeated questions over her response to the alleged incident during Question Time on Thursday at one point becoming visibly upset.
She once again apologised to Ms Higgins expressing remorse that her handling of the matter had added to her "distress".
"I'm deeply sorry that Brittany felt unsupported at the time of the incident and in the months that followed," she told the Senate on Thursday.
"Throughout this entire time, my sole desire has been to let Brittany herself determine how this matter would be dealt with."
Senator Reynolds has known about the alleged rape for more than two years but did not inform Prime Minister Scott Morrison.
Mr Morrison claims his office was not told about the complaint until last week and that he himself only found out about the alleged incident on Monday.
This disputes Ms Higgins' own account who claims members of his staff were aware of the complaint, including one staffer who was Senator Reynolds’ acting chief of staff at the time.
Mr Morrison on Thursday said he never intended to cause Ms Higgins further distress after she accused the prime minister of adopting continued "victim-blaming rhetoric".
"The last thing I would want to see is to add any further distress to what Brittany is already going through," he told Parliament.
"I am very sorry she feels that way. She has shown great courage and bravery in speaking up over these matters."
Mr Morrison has conceded his government mishandled its response to the alleged incident leaving Ms Higgins feeling increasingly isolated in its aftermath.
Ms Higgins claims she felt pressure at the time to not take the matter further with police over concerns that doing so would impact her career.
Minister for Women Marise Payne said the government's sole intention continues to be supporting Ms Higgins.
"Our only intention is to support Brittany in this very difficult time and to ensure we understand the trauma, the distress that she's experienced and continues to experience," she told reporters.
"It's no-one's intention to cause any further concern."
In a statement on Wednesday, Ms Higgins said the government has "questions to answer for their own conduct."
Greens Senator Sarah-Hanson Young backed Ms Higgins' concerns over its response to her rape allegation.
"She feel like she's being blamed, story over," Senator Hanson-Young told reporters.
"The question here is why is the Prime Minister and the Prime Minister's office so desperate to keep this covered up.
"Why don't they just admit what happened? They bungled it."
Mr Morrison has written to Opposition Leader Anthony Albanese, agreeing to develop an independent review into the workplaces of federal parliamentarians and their staff.
He has also ordered internal reviews into workplace culture and complaints handling within the Liberal Party.
With reporting by Tom Stayner
If you or someone you know is impacted by sexual assault, you can call 1800RESPECT on 1800 737 732 or visit 1800RESPECT.org.au.
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