The murder of primary school teacher Ashling Murphy has "united the nation in solidarity and revulsion", Ireland's prime minister has said.
The 23-year-old 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.
PM Michael 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 and 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."
His comments came as Ireland's deputy premier said society has to face up to an "epidemic of violence against women", with senior politicians promising everything would be done to bring the killer to justice.
Justice minister Helen McEntee tweeted: "Every resource will be provided to An Garda Siochana to find who murdered Ashling Murphy. It is vital that we all support the Gardai in their work."
She urged anyone with information to contact the police and shared a picture of a bicycle, which police have asked anyone with information about to come forward.
It's a Falcon Storm mountain bike with straight handlebars and distinctive yellow/green front forks
The murder has triggered widespread outpourings of grief and anger, with vigils planned in towns and cities across Ireland on Friday and over the coming days.
It has also sparked fresh debate about the safety of women in Ireland, with many asking how such an attack could happen in broad daylight.
The family of Ms Murphy have described Ms Murphy as a "special girl" and a "little angel".
Man released after questioning
The solicitor of the man who was released told the PA news agency that he has had his "life ruined".
Donal Farrelly, who represented the man during his two days of questioning, condemned those who had tried to identify him on social media.