Taoiseach Leo Varadkar has said that the people involved in rioting in Dublin city centre last night "brought shame on Dublin, brought shame on Ireland, and brought shame on their families and themselves".
Mr Varadkar expressed his full confidence in Garda Commissioner Drew Harris, however he said a review would also have to be conducted in relation to what happened yesterday.
The Taoiseach said that innocent children were attacked yesterday afternoon.
A five-year-old girl remains in a critical condition in hospital following the attack outside a school in Parnell Square in Dublin yesterday afternoon.
Two other children and a carer for the children also sustained injuries in the stabbing incident.
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Mr Varadkar told reporters this morning that the individual who carried out the stabbing attack was "intent on murder". He paid tribute to "heroes" on the street who intervened, many of whom had different nationalities.
Violent disturbances broke out in the city centre following the knife attack. The Garda Commissioner said that 34 people were arrested following "huge destruction by a riotous mob" in Dublin last night.
Commissioner Drew Harris said a significant number of rioters attempted to breach the cordon of the crime scene on Parnell Square East, following the knife attack.
At least one garda suffered a serious foot injury in last night's violence, Mr Varadkar said.
'This is not who we are as a people' - Martin
Tánaiste Micheál Martin also condemned the rioting in Dublin, saying "this is not who we are as a people".
Mr Martin said in the first instance his thoughts are with the families of the children and adults who were injured in a knife attack.
Turning to the later rioting, Mr Martin acknowledged people are "obviously very, very concerned" about "the lawlessness and the rioting that occurred last evening in our city".
"And I would say that this is not who we are as a people, Ireland has built a modern and inclusive society," he said.
"It is something precious that we should all work to hold.
"We understand the need to respect other, the need to respect difference and the need to respect the dignity of every human being. This is something that we should hold precious and we should collectively as a society come together to recommit to those fundamental values."
The Tánaiste described last night's riots in Dublin as an attack on the fundamental freedom of our citizens.
Mr Martin said the nature of online communications, in terms of the hatred and bile that can often be seen there, is something that must be examined in the days and weeks ahead.
The Tánaiste said he has confidence in An Garda Síochána, the Garda Commissioner Drew Harris and the Minister for Justice Helen McEntee.
He said people have no time for the type of lawlessness seen last night and said that when you attack buses, the Luas and shops "you're attacking your own community, your family, friends and workers".
Support for school staff, children after knife attack - Foley
Minister for Education Norma Foley has said the Department of Education's psychology team is in Coláiste Mhuire following yesterday's attack offering support to the children, staff and school community.
"We are shocked beyond measure. That such an incident could unfold in Parnell Square and our NEPS teams, the National Education and Psychological Service teams, are on the ground in the school. They were there throughout yesterday. They will be available to the school again today and they will consistently work with the school staff to support the school community.
"Every school has a critical incident plan. We would hope that they never have to invoke it, but it was invoked yesterday and the NEPS team go in to support the team within the school to support each other and to support the children.
"I think best practice tells us that at a time like this, children need to be with people that they know best and that are calm a secure environment is provided to the children and that's exactly what will be happening in the school."
She said she has spoken to the school principal who is "very appreciative of the great work and support that has been provided by so many.
Ms Foley said that yesterday "there was incredible selflessness. The immediate instinct of everyone, including the carer and the staff in the vicinity, the staff and the school, was to protect the children, to go to the aid of the children.
"It was quite extraordinary that we see such determination to do the right thing for the children in this awful, awful circumstance and really, really do want to acknowledge the carer and the community and, I wish the carer well, the children well and we hope for a very quick recovery for everybody concerned."
She added that: "It's quite remarkable that in the midst of such unexpected, such unprecedented actions in in Parnell Square that the instinct to do right to do good by the passersby, by the staff. It was quite exceptional."
On the riots on the streets last night, she said those actions should be balanced "with the initial reaction" to the stabbing and how passersby and staff tried to protect the children and "to do the right thing".
"What we saw last night unfold across Dublin were the actions of the few not the actions of many, and I think we should see it for what it is.
"They were the actions of a violent few who created chaos, who upended the city, but they are not reflective of the majority. They are not reflective of society, and they do not reflect the actions that were taken by instinct, by all those who were in Parnell Square yesterday.
"I think we should focus on those actions also."
'Gardaí contained rioting to a very small area' - McEntee
Minister for Justice Helen McEntee said "it is important to recognise that gardaí contained this for the most part to a very small area".
She said she acknowledged that "the scenes were incomprehensible for most people. They [gardaí] managed to contain this to a very small area".
"Yes, there were incidents and individual incidents which expanded out beyond the O'Connell Street area on Henry Street, but this was for the most part contained and by midnight last night, order had been restored to our city.
"But this was a group, a violent mob of thugs and criminals whose sole focus was to wreak havoc. There were a huge number of gardaí, who were assaulted, who were spat at, who were the victims of vitriol and hate themselves."
"And we need to protect them and keep them safe, and I cannot commend them enough."
