Irish police are continuing to hunt for the killer of Ms Murphy, who was found dead after going for a run along the Grand Canal in Tullamore.
Vigils took place across Ireland and beyond on Saturday in memory of 23-year-old Ashling Murphy following the murder of the Co Offaly teacher.
Irish police are continuing to hunt for the killer of Ms Murphy, who was found dead after going for a run on the banks of the Grand Canal in Tullamore.
The Garda said it had made “significant progress” in its investigation, but were not releasing details for operational reasons.
It is understood that gardai have identified a new person of interest, who is believed to be in hospital in the Dublin region, and are waiting to speak to him.
Park Run runners in the Republic of Ireland and Northern Ireland held moments of silence on Saturday morning for Ms Murphy.
Later, people gathered at locations across Ireland on Saturday afternoon to remember Ms Murphy, with hundreds attending a vigil in Cork on Saturday morning.
Vigils have spread beyond Ireland in recent days, with events organised in Glasgow and Edinburgh, as well as in Brisbane, Australia.
At a vigil in north London on Saturday, people held candles and stood in silent tribute outside the London Irish Centre.
Traditional music was played in honour of Ms Murphy, a talented fiddle player, while some of the crowd quietly sang or hummed along.
Anna Johnston, cultural officer at the London Irish Centre, said people had come together in solidarity with those who knew and loved Ms Murphy “and all the women of Ireland and further afield who are angry, distressed and heartbroken”.
Addressing the crowd, she added: “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.”
The vigils come amid widespread calls for an end to violence against women.
Activist and former TD Ruth Coppinger called on Saturday for a “major conference” on gender-based violence.
“This is a watershed moment that must be tapped and lead to meaningful change,” she said.
Thousands of people gathered in the late afternoon in Tullamore, Dublin, and Belfast on Friday, as Ireland continues to reel from the murder of Ms Murphy.
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 When You Were Sweet Sixteen.
Mr Murphy, along with his wife Kathleen and daughter Amy walked on the opposite side of the canal to where his daughter was assaulted and died on Wednesday.
Politicians have promised that all resources necessary will be provided to the gardai to find the killer.
Taoiseach Micheal Martin said that the murder has “united the nation in solidarity and revulsion”.
“No stone will be left unturned in terms of bringing this investigation to a completion and to bring the person responsible for this to justice,” he said on Friday.
On Saturday, the man released by Irish police investigating the murder of Ms Murphy told local paper The Offaly Express of his “horrific experience”.
“I feel terrible for the misfortune of the young woman and the family. I can’t even imagine what they are going through,” Radu Floricel, who was declared no longer a suspect by gardai on Thursday, told the paper.