The prime minister denounced those who participated in the riots and said that the Irish government will modernize its hatred laws to reflect the social media age, according to Reuters.
"We will pass new laws in the coming weeks to enable the Gardai (police) to make better use of the CCTV evidence they collected yesterday, and also we will modernize our laws against incitement to hatred and hatred in general," Varadkar told reporters during a Friday news conference.
"I think it's now very obvious to anyone who might have doubted us that our incitement to hatred legislation is just not up to date. It's not up to date for the social media age. And we need that legislation through within a matter of weeks."
While the prime minister had strong wording against those involved in the civil unrest, Varadkar has not yet addressed the concerns surrounding why the riots sparked off in the first place; which is the public safety impact of allowing mass migration.
Reports claim that the male suspect, 40, is an immigrant of Algerian descent. Police said that he approached the victims around 1:30 p.m. on Parnell Square East. The suspect used a knife to attack a woman in her 30s, before going after the three children, aged five and six, according to RTE.
The woman and one of the 5-year-old girls are in serious condition.
Not long after the attack, protesters took to the streets of Dublin and called for the end to mass migration. The demonstrations started out peaceful but descended into civil unrest by nightfall. Vehicles were burned, and the city center was turned into a battleground as riot police came in to deal with the crowds.
Police arrested 34 people involved with the riots and Irish Garda Commissioner Drew Harris referred to those wreaking havoc in the streets "hooligans" driven by "far-right ideology."
On Friday, the Prime Minister came under fire over recent comments he made to legislators. Vardkar said that Irish institutions are "very white" and that it "needs to change." Ireland has a 94.1 percent white population.
Prime Minister Vardkar, who is the son of an Indian immigrant, admitted more than 120,000 immigrants into Ireland last year.
The knife attack suspect has been detained but his identity has not yet been released.