A number of vigils are taking place across the country today to remember 23-year-old Ashling Murphy, while large crowds also turned out at the London Irish Centre in the UK to pay their respects.
Vigils were also planned for Edinburgh, Glasgow and in Brisbane, Australia.
Ms Murphy was attacked and killed on the banks of the Grand Canal in Tullamore, Co Offaly, on Wednesday afternoon.
Gardaí are waiting to interview a new person of interest in the case who is currently in hospital. A number of searches have been carried out in Tullamore and Dublin as part of their investigation.
Around 5,000 people attended a vigil and walk in Cork this morning.
Director of Cork Sexual Violence Centre, Mary Crilly, described the turnout at the Atlantic Pond near Páirc Uí Chaoimh as phenomenal.
She said a cultural change is needed to remove the threat to women in communities.
Organiser Susan Huggins said she wanted to hold an event to finish the walk or run which many women do not get to finish because of violence.
In Ms Murphy's native Co Offaly, two walks took place this morning along the Grand Canal in Rhode and Edenderry in her memory, while hundreds of people attended vigils in Portumna and Oranmore in Galway.
A vigil was also held in memory of Ms Murphy in Dublin's Smithfield Square this afternoon.
The rally, organised by the Socialist Feminist Movement ROSA, was addressed by a number of women and a piece of music was performed by the former MEP Joe Higgins.
The former Socialist TD and ROSA activist Ruth Coppinger said the public reaction to Ashling Murphy's death was unprecedented and that groups across society now must come together to decide how to take action.
"I think this is a watershed moment. The grief and anger has to be tapped into to make real and qualitative progress on the issue of gender-based violence," said Ms Coppinger.
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Crowds turn out at London Irish Centre to pay tribute
A huge crowd gathered in London this afternoon in solidarity with the family and friends of Ms Murphy.
People held candles and stood in silent tribute outside the London Irish Centre in memory of Ms Murphy.
The large number of people queued in Camden Square, north London, to sign a book of condolence and lay flowers.
The vigil took place at around 4pm - the time at which gardaí said the fatal assault occurred on the banks of the Grand Canal in Tullamore.
Traditional music was played in honour of Ms Murphy, a talented fiddle player, while some of the crowd quietly sang or hummed along.
A minute's silence was held, after which the young teacher's favourite song, When You Were Sweet Sixteen, was sung.
Her father had played the tune on the banjo in tribute to his youngest daughter at a vigil yesterday near the scene of her murder.
Last year in London, people gathered in memory of marketing executive Sarah Everard and school teacher Sabina Nessa - two women who were fatally attacked while out walking in the capital.
A small sign near the entrance to the London Irish Centre bore their names and those of other women who have died, under the letters RIP.
Tens of thousands of people turned out at vigils across the country yesterday, including one in Tullamore attended by Ms Murphy's family.
The family thanked the public for their support and have appealed for privacy.
Reporting: Sinéad Hussey, Paschal Sheehy, Samantha Libreri, PA