1000’s of individuals have been gathering to pay tribute to the 23-year-old, who was discovered useless on Wednesday.
She had been going for a run on the banks of the Grand Cana in Tullamore, County Offaly.
Memorials are being held there and in lots of different cities and cities, together with Dublin and Belfast.
Ms Murphy died from strangulation and Irish police are nonetheless looking for the proficient musician’s attacker.
The Garda mentioned it had made “vital progress” in its investigation however was not releasing particulars for “operational causes”, including that the Murphy household had been “overwhelmed” by the nationwide outpouring of assist.
A 40-year-old man arrested following her homicide has been launched with out cost and is not a suspect.
Gardai imagine the assault was “random” and at the moment are in search of a mountain bike they imagine was linked to the killer.
Irish Justice Minister Helen McEntee mentioned she was “considering of Ashling and all ladies who’re and have been victims of violence”.
“We should come collectively to demand zero tolerance of violence towards ladies. As minister for justice, I’m working to make sure we’ve a society that doesn’t tolerate this any longer,” she mentioned.
Taoiseach Micheal Martin was amongst those that stood in silence outdoors the Dail parliament in Dublin on Friday, whereas Northern Eire’s deputy First Minister Michelle O’Neill joined the gang at Metropolis Corridor in Belfast.
Extra vigils and memorial occasions shall be held within the days to return.
In Tullamore, outlets, companies and cafes closed early on Friday, as hundreds attended a vigil in an area park.
There have been tears as folks got here to mourn and pay their respects to the instructor. Ms Murphy’s mates had been among the many conventional Irish musicians who performed on the vigil.
Attracta Brady, Ms Murphy’s first fiddle instructor, mentioned: “She was essentially the most stunning lady inside and outside.
“She was a guardian’s dream. She was every little thing you’d need in a daughter. She had integrity, she was sincere, she was reliable. She was quirky and a bit of bit cheeky typically… and he or she’d get away with it as a result of she had this stunning twinkly smile.
“She was by no means in unhealthy humour, she was at all times smiling and he or she completely cherished her fiddle. Her mother and father solely informed me yesterday that she by no means needed to be informed to practise. She was vibrant and energetic and everyone cherished her.”
Native priest Father Joe Gallagher addressed the gang earlier than calling for a minute’s silence.
“We bear in mind her heartbroken household, her colleagues in work, in music, in sport, in friendship and her younger pupils in top quality who cherished their instructor,” he mentioned. “This can be a time of grief past phrases.”
“We stand collectively, united with teams throughout our nation, and certainly past, united with ladies who concern and know the trauma of violence. United in grief, in anger, in shock.”
Earlier, Taoiseach Mr Martin mentioned the homicide had “united the nation in solidarity and revulsion”.
“No stone shall be left unturned” in bringing the wrongdoer to justice, he promised.
Ms Murphy’s demise has sparked recent debate concerning the security of girls in Eire, with many asking how such an assault may have occurred in broad daylight.
Tanaiste Leo Varadkar mentioned: “We, as a society, have to withstand this. There’s an epidemic of violence towards ladies. It’s been happening for millennia, fairly frankly.
“Males and boys I believe, particularly, have a accountability to begin to have that dialog amongst ourselves concerning the sort of components, the sort of attitudes, that give rise to emotions that engender males to commit acts of violence towards ladies.”
Gardai proceed to attraction for witnesses and have requested anybody with details about a Falcon Storm mountain bike to return ahead. It had straight handlebars and distinctive yellow-green entrance forks.
Ms Murphy’s household described her as a “particular lady” and a “little angel”.
Her father Raymond informed The Irish Unbiased: “She was an amazing employee, with nice drive. A marvellous musician.
“She crammed a lot into her brief life.”
Floral tributes have been left outdoors the gates of Durrow Nationwide College, the place Ms Murphy taught. She was cherished by her pupils, and workers described her as “a really skilled and proficient younger instructor”.
They mentioned they had been “completely devastated by the passing of our expensive colleague and pal”.