Speaking on RTE radio Sinn Fein's Martin McGuinness said it was very clear from Tony Blair's recent speech that his government had "yet to implement the Good Friday Agreement" which had "created a difficulty" and that the political institutions were effectively "in suspension."
He said he thoughtthat was the context in which the statement had come.
Mr McGuinness called on both Governments as a matter of urgency to recognise the importance of bringing about a process of political dialogue to face up recent difficulties.
The Ulster Unionist Party leader David Trimble said the Provisionals' move justified suspension of the Stormont Assembly.
"It has been obvious for months that the IRA has not been making progress ondecommissioning," he said.
"They are in breach of their obligations under the Agreement and haverepeatedly broken their promises to the people of Northern Ireland.
"This move further vindicates our decision to force the suspension of theinstitutions. It underlines what the republican movement has to do."
Police on both sides of the border said they were disappointed at the IRA'sdecision to withdraw from the arms decommissioning body.
Police Service of Northern Ireland chief constable Hugh Orde and GardaSiochana commissioner Pat Byrne were given the news minutes after aGaelic football match between the two forces.
Mr Orde said: "I am disappointed but like all these movements towards peaceone step forwards may be half a step backwards.
"We will deal with that and move on."
Asked whether it could have been avoided Mr Orde said it was a political issueand it was for the politicians to deal with
He said that in the meantime it was the job of his officers to carry onprotecting all the communities in Northern Ireland.
Mr Byrne said: "It is disappointing but we will just take it in our stride.
"We won't choose to make any interpretation in relation of what it means."This is a bigger issue which I think will find its own level as timeprogresses."
He said it would not change the focus of the police in the Republic at all."Co-operation between North and South is at an all-time high at all levels,"he added.
A Northern Ireland spokesman described the IRA's move as regrettable but nogreat shock.
"While not entirely surprising, since the IRA withdrew co-operation from theIICD after a previous suspension, this is nonetheless a matter for regret," hesaid.
"But the Prime Minister has indicated that the issue now goes far beyonddecommissioning.
"He has made it clear that all paramilitary activity must cease if thepolitical process is to succeed."
Additional reporting PA