Mr Morrison has apologised to Brittany Higgins for the way in which her complaint was initially handled.
"It shatters me that still, in this day and age, a young woman can find herself in the vulnerable situation that she was in, not her doing," he told reporters in Canberra on Tuesday.
We have to do more, whether it's in this workplace or any other workplace in the country, to ensure people can work safely in their place and be at their best and do what they went into that job to do.
Mr Morrison has asked Curtin MP Celia Hammond, a former university vice chancellor, to work with party whips and MPs to improve workplace standards and protect staff.
Department of Prime Minister and Cabinet deputy secretary Stephanie Foster will also review processes for workplace allegations.
An automatic reporting obligation to department officials will be established.
Ms Higgins alleges she was sexually assaulted by a male colleague in the office of federal Liberal minister Linda Reynolds after a night out in 2019.
She decided not to pursue a police complaint at the time because she felt pressure that doing so would affect her employment.
Ms Higgins has since resigned from her job and plans to reinstate the police complaint. She also intends to initiate a formal complaint with the Department of Finance, which handles work-related complaints from ministerial staff.
The prime minister's office was involved in managing the alleged assault from the beginning. However, Mr Morrison said he was not made aware of the specifics of the allegation until 24 hours ago.
He denied there was a "don't ask, don't tell" policy in his office.
"I can assure you there is no such culture and I'm not happy about the fact it was not brought to my attention," Mr Morrison said.
Senator Reynolds has told parliament she never forced Ms Higgins to choose between her job and making a police complaint.
The minister also expressed regret for setting up a formal meeting about the incident in the same room the alleged rape occurred.
Ms Higgins is the third Liberal staffer to allege she was sexually assaulted by men in the party.
Labor MP Peta Murphy wants an independent body established within parliament to deal with complaints, describing workplace cultures in the building as a systemic and cultural problem.
"It's what we've seen in workplaces around the world and in Australia, when there are power imbalances and no processes to deal with them, then incidents will happen," she told reporters.
"We need to not only show and behave in a way Australians expect us to, we need to make sure Australians are confident there are processes in this place to hold people to account when they don't."
The Greens want to establish an inquiry into the handling of Ms Higgins' complaint and another into any systemic issues at play.
1800 RESPECT (1800 737 732)
Lifeline 13 11 14