Mr Morrison said the announcement followed a discussion with his wife Jenny the previous night and after he considered how he, as a father, would want his daughters to be treated.
"Jenny and I spoke last night and she said to me, you have to think about this as a father. What would you want to happen if it were our girls?" he told reporters.
“Jenny has a way of clarifying things. Always has. And so, as I’ve reflected on that overnight and listened to Brittany and what she had to say.”
Mr Morrison said he wants to make sure "any young woman working in this place is as safe as possible, as I would want for my own daughters".
The Prime Minister was later asked by a reporter why it took discussing the alleged incident "as a husband and father" to take further action.
"Shouldn’t you have thought about it as a human being? What happens if men don’t have a wife and children? Would they reach the same compassionate conclusion?" she asked.
"In my own experience, being a husband and a father is central to me, [to my] human being. So I just can’t follow the question you’re putting," Mr Morrison responded.
"Don't you think yesterday as the leader of this country, that it was time ... that you had to take charge?" the reporter asked again.
"I did," Mr Morrison interjected, going on to say he acted upon reflecting on the interview with Ms Higgins that aired on The Project on Monday night.
"I discussed it with Jenny - she had seen it. And we discussed it. That's how we deal with these things. I think Australians know that I am pretty honest about these matters and I seek to deal with them in an as humanely way as possible, and my family helps to inform that, as I suspect it does most people."
'Like the prime minister, I have a daughter'
Mr Morrison's comments quickly attracted criticism from Labor and the Greens, and saw the #NotJustADaughter hashtag start to trend on Twitter.
Labor MP Julian Hill addressed the Prime Minister's response - and his government's handling of the alleged incident - in parliament later on Tuesday.
"Like the PM, I have a daughter," he said. "But that is completely irrelevant to understanding that violence against women is never acceptable. Rape is never acceptable.
"I’m honestly gobsmacked at the prime minister's comments this morning."
He said Ms Higgins deserved respect, support and dignity - "not only because she is someone's daughter, but because she is somebody".
"Daughters and wives do not exist to teach men to respect women and have empathy," he said.
Mr Hill went on to draw links between Mr Morrison's daughters and the government's detention of two young girls from a Tamil family from the small Queensland town of Biloela on Christmas Island.
"How lucky are we, I suppose, that the prime minister has daughters, not sons?" he said. "But what else could the prime minister learn from empathising with his daughters? I wonder how he would feel if the Federal Court had found his daughter had been denied procedural fairness yet was still imprisoned by his government on Christmas Island?"
Mr Hill was speaking about a Federal Court decision on Tuesday which upheld an earlier decision finding three-year-old Tharunicaa was not given procedural fairness when her application for a protection visa was assessed.
Greens leader Adam Bandt also hit out at Mr Morrison.
"You shouldn't need to consult your wife or have daughters to know that women who have been raped should be listened to, believed and supported," he wrote on Twitter. "Women aren't 'finding themselves in vulnerable situations', Prime Minister. Men are putting them there."
"Note to the PM - women are not chattels," Greens Senator Larissa Waters added in her own tweet. "We have value independent of our relationship to you or any other men."
Ms Higgins thanked Mr Morrison for his apology on Tuesday, but said "it should not have taken my story, or the story of other victim-survivors to air on national television for the Prime Minister - or any member of parliament - to take action."
If you or someone you know is impacted by sexual assault, you can call 1800RESPECT on 1800 737 732 or visit 1800RESPECT.org.au.