A team of over 50 Gardaí has been assigned to the investigation.
Gardaí investigating the murder of Ashling Murphy in Tullamore have vowed to leave no stone unturned in the pursuit of justice.
23-year-old Murphy was attacked and killed while out jogging on
Wednesday afternoon, 12 January.
She was well known in the area as she worked as a primary school teacher and was also involved in the arts community.
Speaking on Thursday morning, Superintendent Eamonn Curley of Tullamore Garda Station offered his department's "thoughts and prayers" for Murphy while issuing an appeal for witnesses.
A 40-year-old man was arrested in connection with the fatal assault and is currently being detained for questioning.
Gardaí were alerted to the incident following a call from a member of the public.
"At [the] scene Gardaí discovered a young woman with serious injuries," said Superintendent Curley on Thursday.
"Medical attention was provided but despite the efforts of the medical team who attended, this young lady passed away. The injuries we believe at this time are consistent with an assault.
"This area here where the crime occurred is popular among Tullamore residents and is widely used for recreational purposes," he added.
"The victim of this crime is Ashling Murphy, a 23-year-old local lady from the Blueball area of Tullamore.
"Ashling was a school teacher in Durrow National School. Our thoughts and prayers are with Ashling's family at this time and indeed the wider community, her teaching colleagues and the children she thought who are without their teacher today.
"Personnel from our family liaison unit are providing ongoing support to the family."
An official murder investigation has been launched.
The scene in Tullamore has been sealed off so that the Garda Technical Bureau may carry out a detailed forensic examination.
The results of a post-mortem examination are also awaited.
A team of over 50 Garda personnel has been assigned to the investigation, including members of the National Bureau of Criminal Investigation.
"No stone will be left unturned in bringing the perpetrator of this crime to justice," said Superintendent Curley.
"At this stage there is no information that the victim and her killer were known to each other.
"From inquiries we have carried out to date we believe this crime was committed by one male who acted alone.
"As part of our investigation to date we have arrested a 40-year-old male and this person is currently detained at Tullamore Garda Station.
"I would like to add that we continue to retain an open mind in this investigation and I would like to appeal to the public for their assistance in that regard.
"Firstly, I would like to thank the public for their cooperation and assistance so far, information received from the public to date has assisted us in reaching the current stage of our investigation.
"I would also like to appeal to anyone who has not yet come forward who was on the Grand Canal Way on Wednesday between 3pm and 5pm. We would like to speak to you.
"We are appealing for witnesses who may have seen any person who was behaving unusual in that area. Any information you have however insignificant you may think it may be we need to hear from you.
"Were you on the Grand Canal way between 3pm and 5pm yesterday or have you any information about this incident?
"Please contact us at Tullamore Garda Station on 0579327600 or any indeed Garda Station, or if you wish the Garda Confidential Line 1800 666111.
"I would like to reassure the public that all any information received will be treated in the strictest confidence.
"Finally, our thoughts and prayers are with Ashling's family at this time."
https://twitter.com/NWCI/status/1481579016851271683
The Women's Council of Ireland will hold a vigil for Ashling Murphy on Friday afternoon outside Dáil Éireann between 4pm and 5pm.
"Women must be safe in our homes and our communities," notes a statement.
"Join us and call for an end to men's violence against women."
Members of the public are encouraged to bring flowers and candles to the vigil.
