Women protested across Australia on Monday against sexual violence and gender inequality, with tens of thousands hitting the streets as outrage grew over rape allegations that have convulsed the conservative government.

The #March4Justice rallies were held in more than 40 Australian cities and towns, with a major demonstration in Canberra following allegations of sexual assault in the nation’s parliament.

Dressed in mostly black, the crowd gathered outside Parliament House holding aloft placards with slogans including “You’re Not Listening”, “How Many Victims Do You Know?” and “I Believe Her”.

Former government staffer Brittany Higgins alleged publicly last month that she had been raped by a colleague in a minister’s office in 2019.

And earlier this month, Attorney-General Christian Porter vigorously denied swirling accusations that he had raped a 16-year-old girl in 1988 when they were both students.

On Monday, Porter launched defamation proceedings against public broadcaster ABC, which first published the allegations against an unnamed senior minister, with lawyers saying the attorney-general was “easily identifiable” in the article and has since been subjected to “trial by media”.

Local media also reported that women in the opposition Labor party had recently set up a Facebook page that details alleged sexual harassment by male colleagues and politicians.

The government has ordered an independent inquiry into parliament’s workplace culture and established new support services for staff.

But critics say systemic change is needed – not just in politics but across Australian society.

Higgins told the crowd in Canberra her story was “a painful reminder to women that it can happen in Parliament House, and can truly happen anywhere”.

“We fundamentally recognise the system is broken, the glass ceiling is still in place, she said.

“We are here because it is unfathomable that we are still having to fight this same stale, tired fight.”

Organisers of Monday’s rallies declined an offer from Prime Minister Scott Morrison to speak with them privately, saying attending a closed-door meeting would be “disrespectful” to alleged victims.

“I think the prime minister, if he really cared about women, really cared about our voices . . . he [could] open the door, walk across the forecourt and come and listen to us,” organiser Janine Hendry told the ABC.

An estimated 10,000 joined the protest in Melbourne, with thousands more in major cities including Canberra and Sydney. Several thousand also rallied in Porter’s hometown of Perth on Sunday.

“Evil thrives in silence,” sexual abuse survivor and Australian of the Year Grace Tame told the crowd in Hobart.

“Behaviour unspoken, behaviour ignored, is behaviour endorsed.”

The #March4Justice is demanding a raft of measures including independent investigations into all cases of gendered violence, a boost in public funding for prevention and the implementation of recommendations from a 2020 national inquiry into sexual harassment at work.

Australia’s parliament has been repeatedly criticised for a “toxic” workplace culture that has allegedly spawned persistent bullying, harassment and sexual assault.