Morrison's comments came just hours after The Australian newspaper and Channel 10 reported allegations and images from an anonymous whistleblower about lewd behaviour by male government staff in Parliament House.
They included the men filming themselves performing solo sex acts, including on the desk of a female Member of Parliament.
One government staff member has been removed from his position, a government minister said on Tuesday.
Morrison described the report as "disgusting" and said he would speak with all government staff members on Tuesday to remind them of their responsibilities.
The ruling Liberal/National coalition has come under sustained pressure in recent weeks following allegations of rape by a Liberal party staff member, including one in the office of a Cabinet minister.
The issue spurred tens of thousands of people to rally around Australia last week and led to a slump in Morrison's standing in opinion polls.
Morrison has sought to defend his government's actions in working to improve gender equality, but on Tuesday he accepted there was broad dissatisfaction.
"I acknowledge that many Australians, especially women, believe that I have not heard them, and that greatly distresses me," Morrison told reporters in Canberra.
"We must do better... we must get this house in order."
However, he offered few concrete proposals to improve the workplace culture in parliament, insisting that changes would be announced in the coming weeks.
One week after refusing to meet thousands of women protesting outside Parliament House, the prime minister promised to do better and admitted some of his responses had fallen short.
He tearfully defended focusing on consulting his wife Jenny and speaking "as a father" when responding to sexual assault.
Mr Morrison's government is under colossal pressure after former Liberal staffer Brittany Higgins said she was raped by a former colleague in Parliament House in 2019.
That triggered a wave of revelations about harassment, assault and sexism, as well as a national protest movement calling for more action.
"I acknowledge that there have been people who haven't been happy with how I have responded in every single way over the course of this last month," Mr Morrison said.
"I am setting about to put that right."
His sombre tone evaporated when Mr Morrison launched an extraordinary attack on a Sky News journalist after he questioned if his job should be in jeopardy over the myriad issues.
"You are free to make your criticisms and to stand on that pedestal, but be careful," he said.
The prime minister claimed he knew about a person at the news organisation who had a complaint against them relating to harassing a woman in a toilet.
"You are not aware of it. So let's not, all of us who sit in glass houses here, start getting into that," Mr Morrison said.
The journalist later revealed a senior media adviser confirmed the prime minister was mistaken and the incident did not concern Sky News.
Mr Morrison will address coalition staff later on Tuesday, while Sex Discrimination Commissioner Kate Jenkins is set to speak to Liberal and Nationals MPs.
After cabinet minister Karen Andrews suggested gender quotas in the Liberal Party, Mr Morrison said he had been open to the idea "for some time".
"We tried it the other way and it isn't getting us the results so I would like to see us do better on that front," the federal Liberal leader said.
Mr Morrison admitted his responses to the furore around the treatment of women in Australia had fallen short.
"These events have triggered, right across this building and indeed right across the country, women who have put up with this rubbish and this crap for their entire lives, as their mothers did, as their grandmothers did," he said.
He said it had been a traumatic month.
"We must get our house in order," Mr Morrison said.
Labor frontbencher Kristina Keneally acknowledged Mr Morrison's mea culpa but questioned why it took five weeks of anger to spark the response.
"What I haven't heard from the prime minister is what he is going to do about that," she told Sky News.
"If the prime minister is serious about making real change ... then let's see some specific actions."
Senator Keneally said quotas for coalition preselection, domestic violence services and closing the gender pay gap were key issues that needed action.
A guard on duty the night of the alleged rape of Ms Higgins office has questioned the prime minister's claim the accused man was sacked because of a "security breach".
Mr Morrison said the accused man was sacked because he had "form", including accessing classified documents in the then defence industry minister's office.
Finance Minister Simon Birmingham insists attending the office out of hours for a non-work purpose while drunk did amount to a security breach, but the guard did nothing wrong.
- AAP and Reuters
