The IRA's latest statement was a declaration of peace, the Sinn Fein president has said.
Gerry Adams said the IRA was "declaring peace"
Gerry Adams said this was now a defining stage in the political process and urged unionists "not to lose this moment".
The DUP's Ian Paisley rejected a deal aimed at restoring devolution because the IRA would not allow a photographic record of decommissioning.
The IRA said it would "not submit to a process of humiliation".
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.
Mr Adams said: "He (Ian Paisley) has to face up to the reality that civic nicety isn't a concession.
"It is not generous not to talk to people - especially over life and death issues especially on the back of an offer like this, which is a declaration of peace.
"Let him test the IRA, if he doubts any of this."
He added: "What is making this all the more difficult is the distractions around presentational matters like photographs.
"What I am appealing for - and some may say I am na´ve in asking this - what I am appealing to Ian Paisley to do as the leader of unionism, as a mandated political leader, is to come and meet and talk to me about all of those issues."
However, he said there was "huge trauma" within republicanism.
Earlier on Wednesday, the IRA said demands for photographic proof of decommissioning were "never possible".
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.
Secretary of State Paul Murphy has briefed the Commons on the failed negotiations for devolution.
Mr Murphy said: "I am
absolutely convinced that the day when the final piece of the jigsaw can be put
in place is not far off."
He said there had remained an outstanding issue "which could not be resolved".
"That is the transparency with which the decommissioning process should be carried out," he told the House of Commons.
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.
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."
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.
The issue of weapons continues to be a stumbling block
"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."
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.
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.