Mr Morrison has also fuelled speculation he is poised to shift Defence Minister Linda Reynolds and Attorney-General Christian Porter out of their roles in a reshuffle of his frontbench.
However, Mr Morrison is backing in the besieged pair to remain senior members of his government, saying both will "play a very important role in my cabinet".
It comes as Mr Morrison has ordered an inquiry into whether any members of his staff backgrounded against Brittany Higgins or her loved ones.
The Prime Minister triggered the process after his chief of staff received confidential information from a "primary and direct" source with knowledge of the claims, separate to Ms Higgins herself.
After another day of high drama in Parliament House, A Current Affair host Tracy Grimshaw subjected Mr Morrison to an intense grilling over his government's handling of the alleged rape of Ms Higgins in Senator's Reynolds' office in 2019.
"She told minister Reynolds' chief of staff within days of it [alleged rape] happening, then minister Reynolds was told about it. She told people about it. Why was she on her own? People failed her ..... she was abandoned, wasn't she?" Ms Grimshaw asked Mr Morrison.
In response, Mr Morrison said it was not true to suggest the individuals involved hadn't tried to support Ms Higgins.
However, he said the actions "clearly did not pass the test and failed Brittany".
"No one is disputing that," he said.
"What kept happening and didn't happen is the follow-up service. As she became more traumatised by these events, the services faded away and she was very much on her own."
Asked why nobody had been sacked over the scandal, Mr Morrison said "they would have been trying like everybody else was trying in those circumstances."
Mr Morrison has repeatedly denied he knew of Ms Higgins' alleged rape until it was reported in the media, despite a number of ministers and senior staff having some prior knowledge.
The Prime Minister also faced questions about Mr Porter, who has been on mental health leave since outing himself as the cabinet minister accused of an historical rape allegation.
Mr Porter denies the allegations and has launched a defamation claim against the ABC over reports on the case.
Questioned on why he had simply believed Mr Porter's account, Mr Morrison said police had decided not proceed with an investigation into the incident.
When reminded that police hadn't been able to conduct an investigation because the accuser was dead, Mr Morrison said "what I have done is to respect the rule of law in this country and how people need to be treated under that rule of law".
As the interviewed turned to the broader fallout to Ms Higgins' allegations, Ms Grimshaw expressed disbelief when Mr Morrison suggested the enormity of sexism in society hadn't dawned on him until the past month.
"Where have you been!" exclaimed Ms Grimshaw.
Earlier, Mr Morrison told Parliament had had asked his chief of staff to "commence a process in accordance with advice from the Department of Finance for dealing with complaints against staff members.
Ms Higgins has also made a formal complaint to Mr Morrison's chief of staff, asking him to investigate whether anyone in the prime minister's office tried to privately undermine her loved ones.
The former Liberal staffer wrote to John Kunkel after the prime minister suggested nobody from the parliamentary press gallery had raised the accusations with his chief of staff.
Mr Morrison has previously been asked more than a dozen times in the parliament whether he has investigated the allegations.
He was asked again during a radio interview on Thursday whether he could say categorically his office had not engaged in such behaviour.
"Nothing has been raised with my office from anyone in the gallery making any of those accusations or any discomfort about anything that my office has done," he told the ABC.
"People make allegations all the time second, third-hand. But there's no one who has raised that with my chief of staff out of the gallery, no."
Shortly after his comments, Ms Higgins lodged a formal complaint.
"In the days following my interview with The Project regarding my experience in Parliament House, I was made aware by numerous journalists about the backgrounding that was happening to my partner," she wrote to Mr Kunkel.
"To my knowledge, this was being done by staff within the Prime Minister's media team.
"I believe in giving people the benefit of the doubt. It is entirely plausible the Prime Minister did not know that this was happening, however the more relevant point is that it did occur."
Ms Higgins said the backgrounding was reported to her personally by "various sources" at news.com.au, The Daily Telegraph and Network 10.
It was also referenced during an ABC radio interview with a Network 10 journalist and subsequently reported by various outlets.
Ms Higgins has also requested to provide evidence to department secretary Phil Gaetjens, who is running an inquiry into which of the prime minister's staff knew of her rape allegations before they were made public.
The investigation has been put on hold while police investigate the rape allegations.
"It is my express desire to present my evidence to Mr Gaetjens at the appropriate time once the review recommences," Ms Higgins wrote.
The furore engulfing the government was sparked by Ms Higgins coming forward alleging she was raped by a colleague in 2019.
There have since been rape accusations levelled at Attorney-General Christian Porter and revelations of a toxic workplace culture inside Parliament House.
Mr Morrison has not made direct contact with Ms Higgins since she went public, nor offered her job back.
The Prime Minister is also digging in behind Liberal senator Eric Abetz, who is accused of making vulgar comments about Ms Higgins that amounted to victim-blaming.
"Senator Abetz has absolutely denied this completely," he said.
Women across Australia continue to raise reports of inappropriate behaviour with links to politics.
Parliaments in NSW, Queensland, Tasmania and Canberra have each been told of allegations of rape, groping, harassment and slut shaming.
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