The two parties linked to loyalist paramilitaries have rejected an offer by the two governments to take part in political talks in England today.
Following criticism of the format of the negotiations, the Taoiseach and the British Prime Minister decided to re-invite the smaller pro-agreement parties after they had been sent home after the first day of talks on Monday.
However, both the Progressive Unionist Party, which represents the Ulster Volunteer Force, and the Ulster Democratic Party, which is linked to the Ulster Defence Association, yesterday announced that they did not see any point in rejoining the other parties at Weston Park.
The PUP leader, Mr David Ervine, criticised the Sinn Fein president, Mr Gerry Adams, for disregarding the feelings of the unionist community.
"We are at the high-wire stage here where it is being suggested this whole process is about trying to instil confidence in unionism in the process. But what we are getting is an endless list of demands from Sinn Fein.
"We have said to the Prime Minister, `be careful, because that growing shopping list is ending up in pain for unionism' and when we ask Adams to define the causes of conflict, to tell us the price, we don't get an answer except a growing list of demands. Now, either Gerry Adams is oblivious or uncaring about the impact this is having on the unionist community. You simply cannot have a one-sided process," he added.
The UDP leader, Mr Gary McMichael, said his party felt it had no role to play in the search for a formula which could bring stable government to Northern Ireland.
The leader of the Alliance Party, Mr Sean Neeson, said his party would take up the two governments' offer to participate and urged all parties to come up with the political will to reach agreement.
Prof Monica McWilliams from the Women's Coalition said her party was still awaiting clarification on the exact format of today's talks before making a decision on whether to attend. She called for external mediators to be brought in.
"They [the two governments] should consider bringing in an outside mediator - an organisation like the Mediation Network - so we can work on a memorandum of understanding and towards the implementation of the agreement. We need something new because clearly the talks, as they are, are not working," she concluded.