Updated 1.15pm

A Garda investigation into the killing of Ashling Murphy could go in “multiple directions,” according to former Assistant Garda Commissioner for Dublin Dr Pat Leahy.

Gardaí are continuing to hunt for the killer of the 23-year-old schoolteacher from Co Offaly, after releasing a man they had been questioning late on Thursday night, stating he was “no longer a suspect”.

Dr Leahy said investigations are not “linear processes” and that “around the clock” investigative activities always continue in such cases, even when a suspect is being questioned.

He told the Today with Claire Byrne show on RTÉ Radio that the murder investigation so far shows all the hallmarks of a professional commitment to exploring all of the evidence and pursuing the truth.

A “wide net of Garda activity” is under way in relation to the killing, he said.

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“Door to door enquiries will be conducted. You have forensic scientists working on this. You have telephone and CCTV analysts, scenes of crimes experts. Conferences will be taking place and they will be pursuing multiple lines. There will be total commitment on this from the investigating team.

“(Gardaí) won’t see their families for some considerable length of time because they will be totally and utterly committed to pursuing this and delivering justice for Ashling and her family and the community in Tullamore.”

‘Connect two strands’

Dr Leahy urged the public to come forward with information on the case, even if they believe it is of minor significance.

“No matter how insignificant it may appear to you, it may be just what is required to connect two other strands of information,” he said.

“Or if something just doesn’t sit right. There will be people who will notice activities that may be a little bit out of ordinary. Come forward and talk to the gardaí and let them determine whether it is valuable or not. It is something very small that this investigation may turn on.”

Dr Leahy praised the people of Tullamore and Irish public for the support they have shown since the death of the school teacher, whilst extending his condolences to the family of Ms Murphy.

Minister for Justice Helen McEntee said that “every resource” will be provided to gardaí investigating the killing.

“Every resource will be provided to An Garda Síochána to find who murdered Ashling Murphy. It is vital that we all support the gardaí in their work,” she tweeted, urging anyone with information to come forward.

Gardaí issued a renewed appeal for witnesses on Friday morning and asked anyone with information about a “Falcon Storm mountain bike” with “straight handlebars and distinctive yellow/green front forks” to come forward.

Tánaiste Leo Varadkar also said all available Garda resources were going into finding Ms Murphy’s killer, who remains “at large” on Friday.

“I know people in Tullamore must be very worried at the moment because the killer is still at large and I want to assure people that all of the resources of the gardaí are going into making sure that this person is found, and that they’re brought to justice and that people can feel safe again,” he said.

Taoiseach speaks with family

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On Thursday night, officers released a man they had been questioning over the death of Ms Murphy, stating he was “no longer a suspect”.

The man’s solicitor said on Friday 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.

The murder of 23-year-old Ms Murphy in Tullamore on Wednesday has triggered widespread outpourings of grief and anger, with vigils planned in towns and cities across Ireland on Friday and over the coming days.

The Lord Mayor of Dublin has opened a Book of Condolence for the people of Dublin to extend their sympathies to the family of Ms Murphy, which will be available to sign online from today until Friday, January 21st.

On Friday, Taoiseach Micheál Martin said he had spoken with the young woman’s family.

“I just wanted, like everybody across the country, on behalf of the people to express our solidarity with them and our devastation. The fact that a beautiful young woman has been taken from their lives,” he said.

Mr Martin said the murder of Ms Murphy has united the Irish nation in “solidarity and revulsion”.

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“The gardaí are doing everything they possibly can and getting all of their resources to protect people to make sure people are safe, but also to find out and to find the person responsible for this, and to bring that person to justice.

“I can say without hesitation that every effort will be made to bring this person to justice and to keep people safe in the intervening period.”

Mr Martin added that national school teachers are “the bedrock upon which our society was built on. And, in many ways, Ashling Murphy represented and personified the very best of that tradition of national teaching.”

Ms Murphy, a primary school teacher in Tullamore, was killed on Wednesday afternoon while running along the banks of the Grand Canal.

Those who knew her described her as a gifted musician who was loved by her pupils.

Her death has sparked fresh conversations about the safety of women in Ireland, with many questioning how such an attack could happen in broad daylight.

Several hundred people attended a vigil in memory of Ms Murphy in Galway on Thursday night. Many in the crowd brought flowers and candles to the vigil.

Senior Irish politicians promised that justice would be delivered for Ms Murphy’s family and condemned violence against women.

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Ashling Murphy was attacked as she jogged by a canal (Comhaltas Ceoltoiri Eireann/PA)

On Thursday, gardaí promised to leave “no stone unturned” in bringing Ms Murphy’s killer to justice.

Superintendent Eamonn Curley told reporters that around 50 officers are working on the investigation as he appealed for witnesses to come forward.

He said gardaí do not believe Ms Murphy knew her killer and said he is likely a “male who acted alone”.

The murder scene remained closed off at the Grand Canal throughout Thursday as the murder probe continued.

Gardaí also confirmed a post-mortem examination has been completed.

The route along the Grand Canal is often busy and is a popular spot for walkers and joggers.

Floral tributes were left outside the school gates of Durrow National School, where Ms Murphy taught, as the local community reeled in the wake of the attack.

Principal of Durrow National School, James Hogan, said the school community is “utterly devastated”.

He told RTÉ radio Ms Murphy was a “bright light who put a smile on anyone’s face”.

He added: “Ashling was a shining light to the kids and a very professional and talented young teacher.

“She was an inspiration to so many, not just in our school but across the wider community of schools.”

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.”

Declan Harvey, Fianna Fáil councillor for the area, said: “I am devastated.

“I couldn’t sleep last night thinking of it all because it is a place I go all the time.

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“She went there jogging, she does it regularly. I am lost for words.”

Mr Harvey said it is a route that he and his family often walk.

“It’s a lovely area and helps clear your head. It’s a very popular route that everyone takes. People walk their dogs, people with their kids and prams.”