Loyalist paramilitary group the Ulster Freedom Fighters (UFF) has withdrawn support for the Belfast Agreement.
However, in a statement the group says its ceasefire remains intact.
Meanwhile, the Progressive Unionist Party, which represents the rival Ulster Volunteer Force (UVF), has pulled out of the current round of all-party talks in Staffordshire, England.
The annoucement was made by part leader Mr David Ervine at a press conference in Belfast. The PUP left the talks yesterday clearly angry at the lack of progress.
Mr Ervine said: "For the next phase, you should not interpret that the PUP are half in or half out, the PUP are now clearly out."
He pointed out that an IRA statement last year had promised to put its arms beyond use in the context of the removal of the causes of conflict. He said that republicans had repeatedly refused to state what the IRA meant.
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"During the dialogue yesterday it was my responsibility to ask on three occasions of the republican movement to define the causes of conflict. They singularly failed to do so."
The East Belfast Assembly member said: "Not only will republicans not respond to some unionist demands, ie decommissioning, but they have chosen no other formula that would have sent confidence into the unionist community."
The UFF statement says it finds it intolerable that Sinn Féin has gained "concession after concession, yet there is still a growing erosion of our culture and heritage.
"This has to stop, we cannot allow this to go any further. There can be no more concessions to nationalism while the fabric of our loyalist community is torn asunder."
The UFF said: "We can no longer remain silent in our criticism of an agreement which our membership have continuously voiced their opposition to and which the vast majority of the loyalist community have grown to despise."
The news came as the second day of intensive talks in a bid to break the peace process deadlock began in England.
Arriving for the talks at the Weston Park country estate today, Sinn Féin president Mr Gerry Adams and Ulster Unionist leader Mr David Trimble gave a gloomy picture of talks so far.
Mr Adams said participants in the talks needed to show resilience, tenacity, patience and determination.
"When we left last night there was no evidence that that was the case", he told reporters.
But Mr Trimble pointed the finger at Sinn Féin, saying the talks represented the moment of truth for the Northern Irish peace process.
"Sadly, yesterday we didn't see any evidence that the Republicans were prepared to rise to the occasion", he said.
The Taoiseach and the British Prime Minster have both demanded immediate progress at the talks, with Mr Ahern saying: "This is the week where we can try to finish the outstanding issues. If we work together . . . I believe we can come to a successful conclusion."
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