Mr David Ervine has ruled out the Progressive Unionist Party going to the Weston Park talks tomorrow because their structure allowed republicans to come up with "a growing shopping list of demands".
The East Belfast MLA said: "We are at the high-wire stage here where it is being suggested this whole process is about trying to instill confidence in unionism in the process.
"But what we are getting is an endless list of demands from Sinn Féin.
"Now 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," Mr Ervine said.
Mr Ervine, whose party is linked to the UVF and remains supportive of the Belfast Agreement, criticised the current talks format of the British and Irish governments, Ulster Unionists, SDLP and Sinn Féin trying to resolve the arms issue along with policing and demilitarisation.
The format, he noted, had been applied since 1998, and it still failed to resolve the problems in the peace process.
"Let's think about this a moment. How many minutes have David Trimble and Gerry Adams spent together across a table since April 10th, 1998?
"Then ask the question how many minutes have they spent across a table with Tony Blair? It seems they can't lick a postage stamp without the Prime Minister being there.
"This is not the way to run a process."
Mr Ervine and his party, which officially pulled out of the Weston Park talks on Tuesday, were invited last night by the Northern Ireland Office to return to the secluded venue tomorrow when the talks resume after a break for the July 12th celebrations. PA