The Ulster Democratic Party, the UDA's political wing, is seeking another meeting with the British government to discuss its re-entry to the multi-party talks.
The party leader, Mr Gary McMichael, warned that if the UDP was to be excluded for another six weeks it would question the value of rejoining the talks process.
Mr McMichael said: "I believe the government is dragging its heels over the UDP's re-entry to negotiations. The negotiations have only a short life-span and therefore our inclusion is a matter of urgency.
"The suggestion that we may be excluded for six weeks or more is ludicrous and, if that were to play out in practice, I would question the benefit of the UDP rejoining a process which, to all intents and purposes, would have already concluded its business."
Mr McMichael stressed that the talks needed to be as inclusive as possible if there was to be a successful settlement.
Meanwhile, the talks continued at Stormont Castle yesterday. The confidence-building measures committee met in the morning and the business committee met in the afternoon. The talks then closed for the week. They will resume again next Monday, with discussions continuing on Strand One, which focuses on the internal arrangements for the North.
Speaking after yesterday's session, Dr Philip McGarry, of the Alliance Party, urged the British government to offer greater support to religiously-integrated schools as a way of challenging sectarianism.
"A real peace will only be achieved in Northern Ireland when we have succeeded in dealing with sectarian division", he said. "If we continue to ignore it, then the long-term outcome for society is very poor."
The DUP secretary, Mr Nigel Dodds, said yesterday that the British government would demand strong North/South institutions with full executive powers as the price for setting up an assembly. He claimed that the UUP had effectively accepted this deal.
Mr Dodds suggested that an assembly could be "rigged in such a way to ensure that the SDLP would have a permanent veto and that it could only be set up alongside all-Ireland institutions".