Blaming the IRA for the Northern Bank raid has "scuttled" the chance of the organisation disarming, says Sinn Fein's Martin McGuinness.
Last year, the IRA said it would complete decommissioning
The paramilitary group has withdrawn its offer to scrap all of its weapons.
The IRA, which denies claims it was behind the £26.5m Belfast bank raid, said the British and Irish governments had "tried its patience to the limit".
A Downing Street spokesman said they were not surprised by the statement and that the IRA was behind the bank raid.
Irish Premier Bertie Ahern said he did not regard the IRA's statement as particularly negative.
He said it was more a statement of fact that their offer was off the table.
Mr Ahern said there would be no change of focus whatsoever from either the British or Irish governments.
The two governments still wanted to deal with transparency on decommissioning and an end to criminality and paramilitarism.
At a news conference on Thursday, Mr Adams said: "Confrontation is not the way forward - otherwise the peace process could be as transient as Mr Blair's time in Downing Street."
BBC Northern Ireland political editor Mark Devenport said: "Interestingly, here at Stormont Gerry Adams refused to respond to a number questions about whether the IRA ceasefire would remain stable in the future."
Secretary of State Paul Murphy said the issue was not about confrontation, but about ending criminality.
"They (the IRA) have to accept that is what is dealing a great blow at the moment, both to the peace process and the political process in Northern Ireland," he said.
"We told Sinn Fein that they are to go back and reflect upon the points that the governments have made to them - in many ways the ball is in their court - to stop the criminality which is associated with the IRA."
Mr McGuinness, Sinn Fein's chief negotiator, said he did not see a threat in the statement.
"I don't read that in the statement, but the statement is obviously a direct consequence of what I think is a backwards stance of the two governments and I think it is evidence of a deepening crisis," he said.
Chief Constable Hugh Orde said he had read the statement in full and discussed any possible threat of an IRA return to violence with senior colleagues.
"We know they have the capacity. We know they have the capability. I am currently of the view that they do not have the intent," he said.
"I do not think the statement changes that. But I also make the point that this is an organisation that still exists, is well-organised and has not gone away."
Mr Orde, who is briefing the Policing Board on Thursday, repeated his belief that the IRA was behind the Northern Bank raid.
Last year, the IRA said it would complete the decommissioning process within weeks and move into what it called a "new mode".
The Downing Street spokesman said: "The fact remains that it was the IRA that did carry out the Northern Bank robbery and as the prime minister and the taoiseach said on Tuesday, therefore it is the IRA that is the sole obstacle to moving forward."
However, the spokesman made it clear the government does not interpret the statement as a threat to return to terrorism.
Wednesday's IRA statement, which was passed to the An Phoblacht newspaper, said: "Our initiatives have been attacked, devalued and dismissed by pro-unionist and anti-republican elements, including the British government. The Irish government have lent themselves to this.
"At this time it appears that the two governments are intent on changing the basis of the peace process. They claim that 'the obstacle now to a lasting and durable settlement is the continuing paramilitary and criminal activity of the IRA'. We reject this."
DUP leader Ian Paisley said the statement proved the IRA never had any intention of decommissioning in a credible, transparent and verifiable way.
Speaking outside Downing Street after meeting the prime minister, Ulster Unionist leader David Trimble said there was unanimity in blaming republicans for the present difficulties.
"With regard to last night's statement from the IRA, both ourselves and the prime minister are at one in treating that statement with contempt."
SDLP deputy leader Alasdair McDonnell said the statement offered nothing new from the IRA.