Vigils have taken place across the island of Ireland to remember murdered teacher Ashling Murphy.

Gardaí are continuing the hunt for the killer of the 23-year-old, who was found dead on Wednesday after going for a run on the banks of the Grand Canal in Tullamore, Co Offaly.

Ms Murphy's parents Ray and Kathleen, brother Cathal and sister Amy were joined by extended family and friends as prayers were said by Parish Priest of Kilcormac Fr Michael Meade during a vigil at Kilcormac/Killoughey GAA club.

In a statement issued through the gardaí they requested privacy at this time.

Fr Meade said he hoped the family would get some solace from the massive outpouring of love and support during their darkest hour.

"We all remember what a beautiful person Ashling was," he said.

Ashling's friend Ella Flaherty sang The Parting Glass and music was played by Ballyboy Comhaltas. They were joined by Ray and Amy Murphy to play a traditional piece.

President Michael D Higgins paid tribute to Ms Murphy, a primary school teacher who worked at a primary school in Durrow.

He said he had spoken to her family to offer "my profound sympathy and sorrow and sense of loss that her tragic death has meant to so many, but what in particular it must mean to her mother Kathleen, father Raymond, sister Amy and brother Cathal".

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President Higgins said the "young, gifted teacher" represented "the best of her generation".

He urged: "It is of crucial importance that we take this opportunity, as so many people have already done in the short time since Ashling's death, to reflect on what needs to be done to eliminate violence against women in all its aspects from our society, and how that work can neither be postponed nor begin too early."

A photo of Ashling Murphy from her graduation celebration

Thousands of people gathered in the late afternoon in Tullamore, Dublin, Cork, Limerick and Belfast, as well as in many other towns nationwide.

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

"She crammed so much into her short life."

In Tullamore, shops, businesses and cafes closed as the midlands town came largely to a halt as thousands flocked to attend the vigil in a local park.

There were many tears as people of all ages came to mourn and pay their respects to the young teacher.

Friends of Ms Murphy were among the traditional Irish musicians who played at the vigil in Tullamore.

Attracta Brady, who was Ms Murphy's first ever fiddle teacher, described her as a "fabulous musician".

"She was the most beautiful girl inside and out," said Ms Brady.

"She was a parent's dream. She was everything you'd want in a daughter. She had integrity, she was honest, she was trustworthy.

"She was quirky and a little bit cheeky sometimes with the loveliest smile and she'd get away with it because she had this beautiful twinkly smile."

A huge crowd gathered at Arthur's Quay park on the banks of the Shannon in Limerick tonight to pay tribute to Ms Murphy's short life and express solidarity with her family.

She spent four years studying for a teaching degree at the local Mary Immaculate College.

The gathering was organised by the Limerick Women's Network and the 'Together for Safety' group.

Limerick City Councillor Eliza O'Donovan said people had gathered in grief and support to remember Ashling.

She said it was "inconceivable" that women are still living in fear when they go for a walk or a run.

"Ashling chose Limerick to pursue her studies, and by all accounts she was an exceptional teacher. As a community we share our grief and heartache for Ashling's short but vibrant life," she said.

The Director of the National Women's Council, Orla O'Connor, said the attendance of thousands of people at vigils across the country was an outpouring of anger about what needs to change in society.

She told RTÉ's Six One News it was a watershed moment in the approach towards gender based violence.

Taoiseach Micheál Martin was among those who lit a candle at a vigil outside the Dáil, while Stormont's Deputy First Minister Michelle O'Neill joined the crowd at City Hall in Belfast.

More vigils and memorial events will be held in the days to come.

In pictures: Remembering Ashling Murphy

Earlier, Micheál Martin said the murder of the young teacher had "united the nation in solidarity and revulsion".

"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," he said.

An Taoiseach Micheál Martin attending the vigil at Leinster House

The Taoiseach described Ms Murphy as a young talented musician who had her life violently taken and said people's hearts go out to her family and friends, community and pupils.

He said primary teaching is the bedrock on which society is built and she represented the best of that tradition.

The Tánaiste said Ms Murphy's death does cause people to think more about gender-based violence and this is something that men and woman alike need to combat together.

"I think for men in particular, we need to make sure that we understand and that we teach our boys that violence against women is never justified," Leo Varadkar said.

"It doesn't matter who she is, it doesn't matter where it was, it doesn't matter what time of day it is, it is never justified, it is always wrong."

Also today, gardaí issued a renewed appeal for witnesses and asked anyone with information about a bicycle - a Falcon Storm mountain bike with straight handlebars and distinctive yellow/green front forks - to come forward.

Yesterday, officers released a man they had been questioning, saying he is "no longer a suspect".
The man's solicitor 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.

It is believed about 50 Garda officers are working on the investigation and 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 gates of Durrow National School, where Ms Murphy taught, and the school issued a fresh tribute to her today.

In a statement posted on Twitter, the school said it was "utterly devastated by the passing of our dear colleague and friend".

"Ashling was a very professional and talented young teacher. We are deeply saddened by her tragic loss. Our thoughts are also with her beloved family at this sad time."

Talented camogie player who 'gave back' to the parish

The manager of the Kilcormac/Killoughey senior camogie team has said Ms Murphy did not "keep her super talents to herself", but instead "gave all of them back to the parish and to all the smaller kids".

Ms Murphy played with the club from an early age while in primary school and remained a "dedicated member" over the last 16 years, playing at senior level until last year.

Speaking on RTÉ's Morning Ireland, Donal Rigney said: "We are absolutely beside ourselves with grief and sadness, to lose such a gorgeous individual who gave everything back."

He said Ms Murphy was a "multi-talented person who was deeply involved in Ceoltas.

"A brilliant musician. A brilliant camogie player. A brilliant teacher. But she didn't keep all those super talents to herself. She gave all of them back to the parish to all the smaller kids."

A woman places flowers near the Garda cordon on the banks of the Grand Canal in Tullamore

Mr Rigney said: "To lose a friend and neighbour at that age is truly devastating.

"All the kids in our club who came up through the ranks, she gave everything she has back to them both as a mentor, and with our club.

"From a musical point of view, she would have mentored a lot of players in our club, both boys and girls from playing tin whistles to fiddles, which was unbelievable," he said.

Meanwhile, a musician with trad band JigJam and a friend of Ms Murphy said the "whole town is numb" over what has happened.

Jamie McKeogh said the Irish music community is a "tight knit family" and there are a "lot of people hurting".

"It's very hard to comprehend, I think the whole town is numb.

"For something like this to happen is just a crazy thing and no one really can get their head around it," he said.

Additional reporting: Cathy Halloran, Teresa Mannion