The woman has been named as primary school teacher Ashling Murphy, 23, from Tullamore, County Offaly.

She died after being attacked while running along the canal bank at Cappincur at around 4pm on Wednesday.

Superintendent Eamonn Curley said at a news briefing: "At this stage, there is no information that the victim and her killer were known to each other.

"From our enquiries we have carried out, we believe this crime was committed by one male who acted alone."

He said that a 40-year-old man has been arrested and is being detained at Tullamore Garda Station, and that officers retain an "open mind" in the investigation.

He added: "Aisling was a schoolteacher in Durrow National School. Our prayers are with Ashing's family at this time and indeed the wider community, her teaching colleagues and the children she taught who are without their teacher today.

"Immediately following the discovery of this crime, a full-scale murder investigation was launched."

The incident has shocked the country, drawing comments from local councillors and government ministers.

Declan Harvey, Fianna Fail councillor for the area, described Tullamore as "probably the safest place in the world".

"After yesterday, people will be nervous to go down to the canal," he said.

"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."

Justice Minister Helen McEntee tweeted: "My thoughts tonight are with the family of the young woman killed in a truly shocking crime, with her friends and with her community."

Gardai are appealing for information, and asking anyone who was in the Cappincur/Canal walk area of Tullamore before 4pm on Wednesday to make contact with them.