Ireland's Prime Minister Leo Varadkar is demanding Irish citizens not conflate rising crime with the surge of mass migration flooding their nation in the wake of riots stemming from the brutal school stabbing carried out by a migrant.

"I really would ask people to try and avoid connecting crime with migration," Varadkar said in response to Thursday's Parnell Square school stabbing that left at least five people injured.

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"It's not right. Yes, of course, people who are migrants might commit crimes, just as people who aren't commit crimes."

Ireland is a nation receiving hundreds of thousands of migrants and some will commit crimes, but Irish people also commit crimes, including murders, according to Varadkar.

"When I see what happened in Parnell Square, what I see is a suspect, who is a migrant, although a citizen and somebody here for over 20 years," he said. "I see a 5-year-old child in hospital today, both her parents coming from a migrant background, and her born in Ireland."

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Varadkar also pointed out that four of the six individuals who attempted to stop the migrant stabber were migrants themselves.

"It's totally wrong to try and make out that there is a connection between crime and migration based on what's happened on Parnell Street," he said.