The five main parties suspended general election campaigning for the day.
SDLP chief Colum Eastwood said: “The people of Ireland understand the tragic pain of loss that those in Manchester are feeling.
“We stand with the people of Manchester today, unbroken, unbowed and resolutely determined to defeat those responsible.”
He added: “This was a heartbreaking act of barbarism.”
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Ulster Unionist leader Robin Swann said the attackers would not succeed.
“We stand united with the people of Manchester to face down the terrorists who carried out this cowardly act.
“As a parent, I can only imagine the hurt and pain which the parents of the children killed and injured are going through.”
DUP leader Arlene Foster tweeted her condolences.
She said: “Terrorism must never win.”
Sinn Fein’s leader in the north, Michelle O’Neill, said the attack was horrific.
“For something like that to happen while young people are out enjoying themselves is unthinkable.”
Alliance leader Naomi Long said those behind the attacks cannot be allowed to win.
“They try to threaten our very way of life but, in doing so, inspire people to show the best of humanity by presenting generosity and compassion.
“That is proof good will triumph over evil.”