The UK government has played down the IRA's withdrawal of its offer to complete the decommissioning process.
The IRA statement said it remained committed to the peace process
In a statement, the organisation said it had taken the offer to put its weapons beyond use off the table.
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.
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."
Prime Minister Tony Blair and Taoiseach Bertie Ahern met in Downing Street on Tuesday to assess their political options in the wake of the 20 December raid.
However, the spokesman made it clear the government does not interpret the statement as a threat to return to terrorism.
BBC correspondent Mark Simpson said the statement was "more of an IRA tantrum than anything more significant".
The IRA has denied any involvement in the £26.5m bank raid in Belfast.
Wednesday's 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.
"They never had any intention of giving up their criminal empire," he said.
"The IRA had better realise that we will not be bullied or threatened and we will accept nothing less than the complete and utter end of all terror and criminal activity and the decommissioning of all their illegal weaponry in a transparent manner."
Sinn Fein President Gerry Adams said the statement was "evidence of a deepening crisis", one which he very much regretted.
"The two governments have opted for confrontation. They are engaging in the sterile politics of the blame game without any regard for the consequences," he said.
Sinn Fein's Martin McGuinness told BBC Breakfast that he personally had worked for more than 10 years to avoid crisis in the peace process and "very much regretted" the current situation.
Martin McGuinness said there is now a "mighty responsibility" on those involved in the peace process
"This approach by the two governments has effectively scuttled the enormous work that was done in bringing the IRA to agree to participate in what were unprecedented initiatives around the whole issue of going into a new mode", he said.
Mr McGuinness said there was now a "mighty responsibility" on the two governments and on all those involved in the peace process to deal with the current problems and get the Good Friday Agreement implemented on an "inclusive basis".
Senior Ulster Unionist assembly member Michael McGimpsey said the statement was "a thinly veiled threat".
"It is now up to those who support the democratic process, including the prime minister and taoiseach to stand shoulder to shoulder and face this threat down."
SDLP deputy leader Alasdair McDonnell said the statement offered nothing new from the IRA.
"Instead of facing up to the huge damage done to the peace process by the IRA Northern Bank raid, they are engaging in blatant sabre-rattling and wrecking the Agreement further," he said.
Last November, the IRA agreed to allow a Protestant and a Catholic churchman to witness any future decommissioning of its weapons as part of proposals to restore devolved government in Northern Ireland.
However, the plan was abandoned after the Democratic Unionist Party demanded photographic proof of decommissioning, a demand deemed "unachievable" by republicans.