Gardaí have released a man held for questioning in connection with the killing of Ashling Murphy.
The man has been "eliminated" from Garda investigations, gardaí said late on Thursday night, and he is no longer considered a suspect in the case.
A murder investigation is under way following the killing of the 23-year-old teacher as she jogged along a canal in Tullamore.
"The male who was arrested and detained by An Garda Síochána investigating this fatal assault has now been released from this detention," a Garda statement said.
“This male has been eliminated from Garda enquiries and is no longer a suspect.”
Gardaí are continuing to appeal for fresh witnesses and for anyone with information on a Falcon Storm mountain bike with “straight handlebars and distinctive yellow/green front forks” to come forward.
A post-mortem has been completed on the body of Ms Murphy, a Garda statement said earlier on Thursday, but its results “are not being released for operational reasons.”
Entire country 'devastated'
The killing of Ms Murphy has triggered widespread outpourings of grief and anger, with vigils planned in towns and cities across Ireland over the coming days.
In the wake of the killing of the young schoolteacher, the Taoiseach has said violence against women will not be tolerated in Ireland.
“The entire country is devastated and shocked by the violent and barbaric killing of Ashling Murphy, a young woman in the prime of her life,” Micheál Martin said.
Gardaí have said that “no stone will be left unturned” as they investigate the killing of the young woman as she jogged along a canal.
Superintendent Eamonn Curley told reporters on Thursday morning that around 50 officers were working on the murder investigation, as he appealed for witnesses to come forward.
He said that gardaí did not believe Ms Murphy knew her killer and said that he was likely a “male who acted alone”.
Tullamore locals have spoken of a sense of devastation, as well as confusion about the “randomness” of the attack. The scene remains closed off at the Grand Canal as the investigation continues.
Tributes and vigils
Those who knew Ms Murphy have described her as a gifted musician who was loved by the children she taught.
Floral tributes were left outside the school gates of Durrow National School, where Ms Murphy taught first class students, as the local community reeled in the wake of the attack.
School principal James Hogan described the school community as “utterly devastated”.
Dr Labhras O Murchu, from traditional music organisation Comhaltas, said Ms Murphy was “among the finest exponents of the concertina and fiddle and was also learning the uilleann pipes”, adding: “We know that she and her family are at the heart of her local community.
“She was a much-loved school teacher and had so much to offer in so many ways.”
Vigils are set to take place across Ireland in the coming days as people gather in memory of the primary school teacher.
Gardaí are continuing to appeal for anyone with any information on the fatal assault to come forward, especially those who were in the Cappincur/Canal walk area of Tullamore, Co Offaly before 4pm yesterday afternoon.
Anyone with information is asked to contact Tullamore Garda station on 057 932 7600, the Garda Confidential Line on 1800 666 111, or any Garda station.
-Additional reporting by Press Association.