The Ulster Unionist leader, Mr David Trimble, has warmly welcomed Mr Blair's speech, which he said clearly blamed the Provisional IRA for the current political crisis.
"It is good that there is an unambiguous finger pointing towards the IRA and the role of republicans in destabilising unionist confidence. The crucial question is how will the government follow through in terms of what must be done over the next few months."
Sinn Féin did not condemn Mr Blair's comments but gave a cautious reaction. Mr Gerry Adams said: "I clearly want to see an end to all of the armed groups. I have, and our leadership has, a strategy to bring that about.
"But I deal with all of the armed groups. I don't tolerate what the loyalist paramilitaries are doing. I don't tolerate the allegations of IRA activity and I certainly don't tolerate what the British forces or the police service are doing." Commenting on the Provisional IRA's likely reaction he said: "The IRA can read this speech for themselves and will make their own mind up on this."
The Minister for Foreign Affairs, Mr Cowen, said last night it was vital that paramilitaries were immediately "removed from the equation" and that all parties in the North worked towards the full implementation of the agreement.
Trust had to be built between unionists, nationalists and republicans, Mr Cowen told RTÉ's Six One news. "We need to make a quantum leap. I believe in the full implementation of the agreement."
He dismissed Mr Blair's assertion that while Sinn Féin was prevented from entering government in the Republic, unionists were expected to sit around the cabinet table with the party. Unlike the Republic, the North was "a failed political entity", he said.
Sinn Féin's Mr Martin McGuinness called on Mr Blair to outline how he intended to implement the Belfast Agreement's outstanding issues. "In terms of the IRA, what we have to do is recognise that the object of the exercise is to remove all the British and Irish guns from Irish politics and bring about a set of circumstances which would see the end of armed groups."
SDLP Assembly member Mr Sean Farren welcomed Mr Blair's speech. The British Prime Minister had made it clear there was "no alternative" to the agreement. He had also stressed the Provisional IRA had "a responsibility which they have not delivered on".
DUP deputy leader, Mr Peter Robinson, said Mr Blair was attempting to "shore up a crumbling process". He must instead accept the agreement was "both flawed and failed". The absence of sanctions against the Provisional IRA showed how "bereft of a stick" the British Prime Minister was. If Mr Blair was waiting for movement from the Provisionals, "he must do more than beat them around the head with carrots". Alliance leader Mr David Ford said Mr Blair must outline plans to ensure the Assembly was back in operation soon.
"If Mr Blair's main problem is with republican antics, the rest of us shouldn't be left hanging in limbo forever. I welcome the Prime Minister's recognition of the very real problems republican paramilitary activity has brought.
"But Mr Blair cannot expect democrats to wait indefinitely with the institutions suspended for republicans to make up their minds about whether to continue with their twin-track tactics or commit to exclusively peaceful means."
Anti-agreement UUP MP, the Rev Martin Smyth, said unionists must remember Mr Blair's history of "broken promises".
"All we have had are further words. Many of the ordinary decent law-abiding people to which the speech referred will be dismayed that, rather than spelling out what action he would take against the IRA if they did not disband, we witnessed the Prime Minister of the UK pleading with the terrorists to change their ways."