Ms Murphy, 23, was found dead on Wednesday afternoon after going for a run on the banks of the Grand Canal in Tullamore, Co Offaly.

Gardai are continuing the hunt for her killer after a man who was being questioned was released from custody, deemed no longer a suspect.

Taoiseach Micheal Martin said: "It's very poignant and a very sad moment in our nation's affairs when a young talented musician had her life violently taken a few days ago.

"Our hearts and our minds go out to the Murphy family, to her community, to her family and friends, and to particularly the young pupils who no doubt would have been looking forward to Ashling's presence in the classroom teaching music or sport as well as the broader curriculum."

"I've always been of the view that a national schoolteacher, from the beginning of the state, has been the bedrock upon which our society was built.

"And, in many ways, Ashling Murphy represented and personified the very best of that tradition of national teaching.

"I think it has united the nation in solidarity and revulsion at what has happened."

Mr Martin added: "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."

Ireland's deputy premier Leo Varadkar said society must face up to an "epidemic of violence against women".

Mr Varadkar added: "Men and boys, I think, in particular have a responsibility to start to have that conversation among ourselves about the kind of factors, the kind of attitudes, that give rise to feelings that engender men to commit acts of violence against women.

"I would hope that by shining a light on gender-based violence might help us to have this discussion in society and to improve things."

Mr Martin promised a national strategy is being developed to tackle sexual, domestic, and gender-based violence in Ireland, which will adopt a "zero-tolerance" approach.

Vigils have been held across Ireland in recent days and more are planned, as people express their grief for a young woman described by her family as a "special girl" and a "little angel".

Thousands of people gathered late on Friday afternoon in Tullamore, Dublin, and in the Northern Ireland city of Belfast, as well as a number of other towns.

Ms Murphy's father Raymond told the Irish Independent newspaper: "She was a great worker, with great drive. A marvellous musician.

"She crammed so much into her short life."

Man released after questioning

On Thursday police released a man they had been questioning, saying he is no longer a suspect.

But the man has had his "life ruined", according to his solicitor Donal Farrelly, who represented him during two days of being questioned.

Mr Farrelly criticised those who had tried to identify the man on social media.