Protesters have let off flares and fireworks at police as one of the children, a five-year-old girl, and a woman in her 30s are being treated in hospital for serious injuries.

Officers with riot shields are holding back crowds in the city centre where a police car and two double decker buses have been set on fire amid anger over the stabbings in Parnell Square East.

A fire has also broken out inside a damaged Luas tram as violence continues on O'Connell Street in Dublin city centre.

Sky News' Ireland correspondent Stephen Murphy has seen people looting a Foot Locker store in the city during the chaos.

Rioters are attempting to kick and punch police and there are ongoing scuffles, with bottles being thrown.

A Garda public order unit has been deployed to control the disorder.

A five-year-old boy, a six-year-old girl and a man in his 50s were treated in hospital for less serious injuries following the stabbing attack earlier, Superintendent Liam Geraghty said. The boy was later discharged from the Children's Health Ireland at Crumlin Hospital.

In a press conference earlier, SI Geraghty told the media the five-year-old girl was receiving "emergency medical treatment". He also said the stabbing appeared to be a "standalone attack".

Police have said they are not treating the attack as terror-related but are not "ruling out any motive" after the stabbings.

Following the rioting, Garda Commissioner Drew Harris has told journalists outside Mountjoy Garda Station: "I think there's disgraceful scenes in terms of a major investigation, the maintenance of a scene and the gathering of evidence.

"We have a complete lunatic hooligan faction driven by far-right ideology, and also then this disruptive tendency engaged in serious violence.

"We are drafting in resources to deal with that and that will be dealt with properly. I've given full direction to our resources here in respect of making arrests and bringing offenders to justice.

"It's our responsibility to make sure that we police the streets, and part of that is we ask people to act responsibly and not to listen to the misinformation and rumour that is circulating on social media.

"The facts are being established, but the facts are still not clear on a lot of the rumour and the innuendo is being spread for malevolent purposes."

In a statement, Irish justice minister Helen McEntee said: "The horrific attack today in Dublin city centre was an appalling crime that has shocked us all.

"An Garda Siochana are following a definite line of inquiry and are not looking for anyone else regarding this crime. The perpetrator will be brought to justice.

"However, the scenes we are witnessing this evening in our city centre cannot and will not be tolerated.

"A thuggish and manipulative element must not be allowed use an appalling tragedy to wreak havoc."

Irish Prime Minister Leo Varadkar said a suspect has been detained. Earlier, police said they are not looking for anyone else at this time.

Mr Varadkar added later: "The facts in this matter are still emerging.

"The emergency services responded very quickly and were on site within minutes. I thank them for that."

He also said police were following a "definite line of inquiry".

"Five casualties have been taken to various hospitals in the Dublin region," an Irish police spokesperson said.

"An Garda Siochana is in contact with parents of all three injured children."

Stephen Murphy, Sky News' Ireland correspondent, said witnesses have told police they saw a man, who was reportedly wielding a knife, "attack several young people" as they left school.

The school is an Irish-speaking primary school where all students would do lessons in Irish.

"It appears that bystanders and eyewitnesses have played a huge role in bringing this incident to a halt," Murphy said.

"Witnesses have spoken of seeing several bystanders become involved to try and intervene and restrain this man."

He described Parnell Square as an extremely busy area "right in the heart of Dublin city".

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Mary Lou McDonald, leader of Ireland's opposition party Sinn Fein and a representative of Dublin Central, told Sky News: "The community is numbed and horrified.

"This is the last thing you expect to happen on a Thursday afternoon in the middle of Dublin city.

"It's a great school community and people's hearts are with the children who have been traumatised and those who have been injured.

"There aren't actually words to describe how numbed people feel. This doesn't happen in our city at a school as very young people are being collected.

"We pray for their full recovery, and for the parents."

In a post on social media website X, Ms Mcdonald also named the school affected as Gael Cholaiste Mhuire.