Though, she denied the woman was pressured against making a police complaint.
Ms Higgins' allegations have drawn renewed attention to what has always been criticised as a toxic culture for women inside Parliament House.
Morrison promised an investigation in the alleged rape and the culture inside the country's political capital, a day after the former staff went to the media with her story.
'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.
Ms Higgins herself has called for an independent reporting mechanism along with a comprehensive review of the laws that govern ministerial offices.
The woman, Brittany Higgins, did not name the colleague, but said it was someone who worked for Morrison's ruling Liberal party and that she had been raped in the office of Defence Minister Linda Reynolds in March 2019.
"We have Brittany Higgins' own evidence that she felt like a problem to be managed rather than a crime where she was the victim and it should be reported".
Morrison said Reynolds should not have questioned Higgins about her accusation in the same office where Higgins alleged the rape took place.
Tame ended her post with the words, "This is Brittany's story. I was crying. I told him to stop, but he didn't".
She said the man left immediately afterwards, and she wasn't offered assistance by security guards on her way out of parliament.
After arriving at Reynolds's office, Higgins, who was donning a cocktail dress, remembered being exhausted and lying down.
"I understand that over time, particularly in situations like this, that information can become confused over time about who makes contact and things like that", he said.
Political staffer Brittany Higgins then 24 has alleged she was raped by a colleague inside Australia's Parliament House
Though Reynolds told Higgins she would support her in a police case, the victim believed it would end her career.
As the allegations garnered outrage, Morrison apologized to Higgins, specifically for the meeting that took place in Reynolds's office.
"There was a loop happening in my mind of this trauma that I'd just sort of come to terms with and I thought it was unfathomable that they would put me in such a place again", she said.
Ms Reynolds was the defence industry minister at the time of the alleged rape, and became defence minister two months later.
Reynolds echoed Morrison in apologizing a few hours later.
He said such an event "should not have happened", saying it would spark a review of the complaints procedure in parliament. "I want to make sure any young woman working in this place is as safe as possible".
Higgins issued a media statement on Tuesday thanking Morrison for his apology. "What would you want to happen if it were our girls?" he said. Today, our PM, Scott Morrison, is being criticised for his tone-deaf response.
"It should not take a man having a daughter for him to treat women who've been assaulted with empathy and respect", wrote author Jamila Rizvi on Twitter.
Ms Higgins said chose to speak out after being inspired by women's campaigner and Australian of the Year victor Grace Tame. It has previously been accused of covering up sexual misconduct.
Mr Morrison denied his party had a "women problem" before the 2019 general election, after the departure of several female MPs. There will also be a separate probe into workplace culture.
Tame, 26, who was named 2021 Australian of the Year for her advocacy for survivors of sexual assault, is no stranger to the courage it took for Higgins to speak up.
Scott Morrison's response to Higgins' allegations was, at best, unhelpful.
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