Sinn Fein's chief negotiator Martin McGuinness has suggested that any future IRA move on arms should be more convincing for unionists.
Any deal to restore the peace process is likely to involve a third move by the IRA to put arms beyond use in co-operation with the international arms decommissioning body.
Unionists have insisted that the lack of detail from General John de Chastelain's decommissioning body about the last two IRA acts of disarmament has diminished unionist confidence in the peace process.
At the weekend, Mr McGuinness has acknowledged that this is a serious issue for unionists. and said his party was aware that the lack of transparency in past acts by the IRA had caused disappointment.
He said General John de Chastelain had the power to bolster the political process - though how public confidence could be boosted was a matter for the general and the IRA.
"We are not immune to the arguments that are being made, but at the same time we are also conscious that there are people out there in the anti-agreement unionist side who, no matter what is said and done, will not be satisfied," he told BBC Radio on Saturday.
Mr McGuinness said he did not want to damage the "prospect of progressive forces within unionism" in a possible assembly election.
"Let me put it like this - I don't want to see the DUP, I don't want to see the negative forces within the Ulster Unionist Party, moving into the ascendancy," he said.
"I think that would be an absolute disaster for the peace process, a disaster for the Good Friday Agreement."
However, there were further problems for peace efforts after the Ulster Unionist Party's executive effectively rejected the Joint Declaration of the Irish and British governments
The document, proposed in May 2003 as a means of overcoming the current political impasse in the North, contains a plan for the final implementation of the 1998 Good Friday Agreement.
The UUP decision appeared to surprise and dismay the Sinn Fein leadership, which had insisted that the hardline wing of the UUP had been soundly defeated at a recent meeting of the party's ruling Ulster Unionist Council.
The joint declaration included five annexes dealing with demilitarisation, policing and justice, human rights and equality, on-the-run political prisoners and the controversial international monitoring commission, which has also been opposed by Sinn Fein.
The UUP said in a statement that the party would not be bound by the document, which it insisted did not provide "a satisfactory basis for progress".
There were reports of a difficult meeting between the Sinn Fein and Ulster Unionist leaderships at the weekend. Mr McGuinness and the Sinn Fein president, Mr Gerry Adams, expressed their opposition to a new Ulster Unionist resolution when they met the UUP leader, Mr David Trimble, on Saturday, according to the reports.
Mr Adams and Mr McGuinness were said to be annoyed at the motion adopted by the UUP's 110-member executive on Friday calling for "radical change" to the Joint Declaration.
The resolution was being portrayed as a victory for the anti- Good Friday Agreement camp within the UUP, and it appeared that three dissident MP would be returning to the party fold.
Supporters of Mr Trimble, however, have stressed that the motion does not explicitly reject the declaration. Mr Trimble described the motion as "nuanced".
The apprent outbreak of peace within the long-feuding Ulster Unionist Party was being seen by some commentators as a necessary convenience for the expected Assembly election next month. Others, however, believe that the party is quietly moving to an anti-Agreement line, and Mr Trimble's hold on the party leadership is increasingly tenuous.
Meanwhile, British and Irish leaders failed to make any progress in talks on the margins of a European Union Summit over the weekend.
Afterwards, Irish Prime Minister, Taoiseach Bertie Ahern warned that it would be "ferociously difficult" to enter into elections unless outstanding problems in the North were addressed.
Mr Ahern said all sides knew what they had to do to trigger the elections and get the assembly and its power-sharing executive reinstated.
"We really need parties to move into a decision-making stage on this. You can only do so much talking," he said.
"It will be ferociously difficult to go into elections if the atmosphere is not positive and where we can't see our way through it," he added.