Brittany Higgins said she was sexually assaulted by a colleague inside Parliament House.
Mr Morrison, a father of two daughters, revealed he was determined to take action after speaking to his wife about the incident on Monday night. "What would you want to happen if it were our girls?"
During her interview with The Project, Ms Higgins said she had "started that night with a different date" and "invited him in a professional context".
Ms Higgins' rape allegedly happened after she colleagues were on a night out.
After the incident, Senator Reynolds summoned her to a formal employment meeting in the same room the alleged rape occurred.
Ms Higgins said she was drunk and feel asleep in Defence Industry Minister Linda Reynolds' office, before waking to find the man sexually assaulting her.
Senior members of the federal government, including Prime Minister Scott Morrison, have publicly responded to allegations a former Liberal Party staffer was raped in a ministerial office at Parliament House.
Addressing how the meeting between Senator Reynolds and Ms Higgins was held at the scene of the alleged rape, Mr Morrison said: "That should not have happened and I do apologise".
The young staffer said during the meeting with Senator Reynolds she was "nice" and "apologetic", but the meeting quickly turned to whether she would report the incident to police.
"It felt like immediately it became a political problem, it wasn't a staffing problem, it wasn't a human problem, it was like we have an issue", she said.
"The first thing that sort of awoke me, is that I was in pain, my leg was being crushed, the senior staffer was on top of me".
But instead of dropping her home, the man allegedly took her to Parliament House. "But I'm not naive enough - and I don't think any of you are, or frankly anyone else in this place is naive enough - to think that this is not a position of vulnerability that can still occur", he said. "So, I hope Brittany's call is a wake-up for all of us from that point of view".
The prime minister said he was only made aware of the allegations on Monday morning despite the alleged engagement of staff from his office in the investigation.
He denied there was a "don't ask, don't tell" policy in his office.
"That is a very valid question and I can assure you I am not happy about the fact that it was not brought to my attention - and I can assure you people know that", he said.
A spokesperson for the Prime Minister's Office said Ms Higgins was told if she did choose to pursue a complaint, including with police, she would have the support of the Office and the Minister.
He said West Australian MP Celia Hammond, former vice-chancellor of the University of Notre Dame, would now work with Coalition MPs to consider new standards.
Mr Morrison said the environment of Parliament House needed to be addressed.
'It's what we've seen in workplaces around the world and in Australia, that when there are power imbalances and no processes to deal with them, then incidents will happen, ' she told reporters in Canberra.
Department of Prime Minister and Cabinet deputy secretary Stephanie Foster will also review workplace processes in regard to the allegations.