There must be "zero tolerance" of violence against women following the murder of Ashling Murphy, Justice Minister Helen McEntee has said.
Urging anyone with information on the killing to contact the gardaí, Ms McEntee said the wider issue of violence against women, including sexual and domestic abuse, must be tackled.
"We need to take on board what has happened in our society and ensure that there is zero tolerance for violence against women," she said. "This is a priority for me and for this Government.
She said Ms Murphy's murder was "an evil act, and will be treated as such", and that she too had experienced situations where she felt unsafe.
Politicians have said that legislative and cultural change is now needed to tackle gender-based violence, and have called for an overhaul of sexual health education from a young age.
Fine Gael TD Jennifer Carroll MacNeill said a new curriculum based on respect, consent, and personhood is urgently required. She said it could be taught right the way from primary school up, in an age-appropriate manner.
She said: "I drop my little boy to school, and I look at the schoolyard, and any parent dropping their kid has to wonder — what are we going to do that is going to make it different than it was for our generation, for my mother's generation?
"The only thing that we can do to stop that cycle of creating abusers and people who are abused is to try to teach them differently."
Ms Carroll McNeil said: "Until there is a deep shift in terms of how we think about men and women in really egalitarian terms, the idea that women are different or are more vulnerable because they're physically more vulnerable is just going to persist."
This was echoed by Solidarity/PBP TD Paul Murphy, who said there are no "overnight solutions" to gender-based violence, but education and creating more awareness has a massive impact on how women are portrayed and objectified.
He said any new curriculum should also be mandatory, as he pointed to the fact that currently schools can opt-out of sexual education because of their ethos.
"The answer to a woman being murdered can't be calls on women to change their behaviour — that's not the answer," he said.
Fianna Fáil TD for Offaly Barry Cowen said there needs to be an acknowledgement that women do not feel safe.
“I can go for a walk, I’m a man, I feel safe, but women don’t, that’s not equality," he said.
Minister of State Josepha Madigan said the special Oireachtas committee on gender equality due to meet this year must now focus on violence against women.
However, she also suggested that apps and other measures to protect women could be introduced.
"We need to look at practical measures like panic buttons, perhaps," she said, but added that the "root causes", including education in schools, must also be looked at.
Expressing sympathies with Ms Murphy's family and friends, MEP Frances Fitzgerald said: "Every 10 years a city the size of Marseille, Amsterdam, or Zagreb disappears from the world.
"It’s estimated that 87,000 women worldwide are being killed each year just because they are women, this is femicide."