Demands for photographic proof of decommissioning were "never possible", the IRA has said.
The issue of weapons continues to be a stumbling block
The demands of Ian Paisley's DUP were an excuse for rejecting a power-sharing deal which could "remove the causes of conflict", it said in a statement.
The IRA said it was committed to the peace process but would "not submit to a process of humiliation".
Secretary of State Paul Murphy is due to brief parliament on the failed negotiations for devolution.
Prime Minister Tony Blair and Irish premier Bertie Ahern published their proposals on Wednesday after Sinn Fein and the DUP failed to agree a deal which could have revived power-sharing in Northern Ireland.
Mr Paisley refused to sign up because the IRA would not allow a photographic record of it putting its weapons beyond use.
The IRA statement, in which the organisation said it would move into a "new mode", appeared in Thursday's edition of the republican newspaper An Phoblacht.
In the event of a deal the IRA said there would be an end to its activities, complete decommissioning by December "if possible" and that two clergymen would oversee the process.
It added: "For his part, Ian Paisley demanded that our contribution be
photographed, and reduced to an act of humiliation.
"This was never possible. Knowing this, he made this demand publicly as the
excuse for his rejection of an overall agreement to create a political
context with the potential to remove the causes of conflict."
BBC Northern Ireland security editor Brian Rowan said: "What the IRA is signalling in this statement is a process towards its end game."
The Northern Ireland secretary said the two governments had thought they had come up with a compromise in which the photographs would be published when the executive was up and running.
Mr Murphy said: "Consequently, we have got to find a way around this over the next
couple of weeks and whether we can move the process forward."
DUP leader Ian Paisley said the IRA statement showed it "never had any intention of decommissioning".
He added: "Another secret act of decommissioning will not satisfy the public to any degree acceptable.
DUP leader Ian Paisley blamed Sinn Fein and the IRA for the deal's failure
"I believe the IRA's reaction is proof that they cannot and will not be honest about the matter of decommissioning and are therefore not ready for the democratic process neither are they committed to peace."
Ulster Unionist leader David Trimble described the IRA statement as a
"disappointment" and that decommissiong had to be a public act.
"When the first weapons decommissioning occurred in Northern Ireland, which
was decommissioning by a loyalist paramilitary group, it was filmed and we all
sat and watched that night the angle grinders cut up the weapons," he told the BBC's Today programme.
Sinn Fein's Mitchel McLaughlin said: "I think we have a definitive view on the photographs, let's move on, let's forget about them and let's move on to this question of whether unionists who need further reassurance will accept the word of their own witness. "
Church of Ireland Primate Archbishop Robin Eames urged politicians to continue their efforts to reach agreement.
"We are so close to something of historic importance," he said.
Catholic Primate Dr Sean Brady said he was disappointed that a deal was not done.
However, he said politicians must continue to build on the progress that had been made.
David Trimble believes republicans are being "too precious"
Irish Foreign Affairs Minister Dermot Ahern said the issue of photographs was central to the recent negotiations.
He told BBC Radio Ulster the issue was never ruled out by republicans as categorically as they had indicated.
"We knew that the issue of photographs themselves might not be the difficulty, but the publication of the photographs in such a way as would be seen as being as a humiliation or a victory for one side, would not be countenanced," he said.
The government has said it intends to maintain the momentum after hopes of a deal were dashed.
Renewed talks between the governments and the parties will be held next week.
Speaking in Belfast on Wednesday, Mr Blair said "remarkable" progress had been made towards an agreement, but it was not yet complete.
The potential deal could have led to the restoration of Northern Ireland's political institutions, which were suspended in October 2002 amid claims of IRA intelligence-gathering at the Northern Ireland Office.
As the agreement broke down, DUP leader Ian Paisley said Sinn Fein had "pulled the plug" on the deal.
He said "significant progress" had been made on all aspects of the comprehensive agreement with the exception of how decommissioning would be handled.
Sinn Fein President Gerry Adams said the issue of photographs of decommissioning was first raised with the party in the week before the Leeds Castle talks in September.
He said: "We were told by the two governments that this was a DUP demand and we told the governments, in our view it was not achievable."
The secretary of state and the Irish Foreign Minister, Dermot Ahern, are now planning to hold meetings with all the parties to try to assess the way forward.
The two prime ministers are also expected to meet next week to agree their joint strategy.