Runners across Ireland and London have stopped to remember Ashling Murphy whose murder has shocked the nation.
Irish police are continuing to hunt for the killer of the 23-year-old primary school teacher, who was found dead after going for a run on the banks of the Grand Canal in Tullamore, Co Offaly.
The Garda said it had made "significant progress" in its investigation but were not releasing details for operational reasons.
It is understood investigators have identified a new person of interest, who is currently in hospital, and are waiting to speak to him.
Park Run participants in the Republic and Northern Ireland stood in silence on Saturday morning in memory of Ms Murphy.
More vigils in Cork and London
Hundreds of people also gathered in Cork for a vigil, with more planned in towns and villages over the weekend.
In London, hundreds more gathered outside the London Irish Centre in Camden.
Mourners held candles and staged a minute's silence at 4pm - the time police say the fatal attack happened - which was followed by the teacher's favourite song When You Were Sweet Sixteen.
Addressing crowds, cultural officer at the centre Anna Johnston said: "Today, along with Ashling, we remember all the women who have had their lives stolen through gender-based violence. We shouldn't be here, and Ashling should be."
Meanwhile in Ireland, deputy prime minister Leo Varadkar said: "For men, we need to understand, and to teach our boys, that violence against women is never justified.
"It doesn't matter who she is, where she was, what she was doing and it doesn't matter what time of the day it is. It's never justified. It's always wrong."
Show of solidarity
The show of solidarity came after thousands of people gathered on Friday in a united show of grief and revulsion at the murder, which has been described as a "watershed moment" in the campaign to end violence against women.
Ms Murphy's family attended a candlelit vigil near the murder scene on Friday evening.
At the event, her father Ray Murphy paid a poignant tribute to the talented young musician by performing her favourite song on the banjo.
He broke down in tears while playing the final chords of her favourite song.
Mr Murphy, along with his wife Kathleen and daughter Amy, walked on the opposite side of the canal to where his daughter was killed on Wednesday.
Murder sparks fresh debate about violence against women
Politicians have promised that all resources necessary will be provided to the police to find the killer.
The death of Ms Murphy has sparked a renewed debate about the safety of women in Ireland, with many asking how such an attack could happen in broad daylight.