One was held on the steps of Derry’s Guildhall Hall from 4 pm.
The 23-year-old was attacked on the banks of the Grand Canal outside Tullamore, County Offaly, on Wednesday afternoon and died at the scene.
A 40-year-old man arrested over her murder has been released “and is no longer a suspect”, police said.
A number of politicians attended the event in Derry’s Guildhall Square, including the SDLP leader Colum Eastwood and the Mayor of Derry and Strabane Alderman Graham Warke.
One speaker at the Guildhall said: “We cannot stop until women are safe to exist freely.
“May your story inspire rebellion for the protection of women everywhere.”
Another said: “The police tell us being drunk is “asking for it,” what culture are we living in, what culture?
“Women are not the problem, we have never been the problem.”
Some mourners held signs with one reading: ‘Misogyny is murder.’ Candles and flowers were placed at the steps of the Guildhall.
One of those is being held outside the Oireachtas buildings in Dublin.
It began at 4 pm and Taoiseach Micheál Martin was among those in attendance.
He said Ms Murphy was a talented musician who “represented the very best of the tradition of teaching in Ireland”.
The Taoiseach also said no stone would be left unturned in the investigation.
“I think it has united the nation in solidarity and revulsion at what has happened,” he added.“We have to do everything that we possibly can to eliminate this appalling behaviour from our society.”
Ms Murphy’s family have spoken of having lost “a little angel” and “our rock” in an interview with the Irish Independent newspaper.
Her father, Raymond, told the paper of his daughter’s talent for music and how she had “crammed so much into her short life”.
Her mother, Kathleen, added that “she was so soft and gentle”.
“She was a beautiful girl, she was just the best,” she said.
“We’re all devastated.”
President Michael D Higgins said he had spoken to the Murphy family on Friday morning to express sympathy on behalf of the people of Ireland.
“The outpouring of grief at the death of Ashling shows how we have all been very touched, and it is so exemplary for young and old, to read of all Ashling’s accomplishments during her short but brilliant and generous life,” he said.
“It is of crucial importance that we take this opportunity, as so many people have already done in the short time since Ashling’s death, to reflect on what needs to be done to eliminate violence against women in all its aspects from our society.”
On Friday morning, gardaí renewed their appeal for information about the murder.
Detectives have previously said they believed she was killed by one man who acted alone.
A team of more than 50 officers has been assigned to the murder investigation and an incident room has been set up in Tullamore.
“No stone will be left unturned in bringing the perpetrator of this crime to justice,” said Supt Eamonn Curley on Thursday.
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