Mr Paisley, as leader of the Democratic Unionist party, handed in a three- page "indictment" of the smaller loyalist groupings, complaining that they had failed to condemn the paramilitary death threat against Portadown militant loyalist Billy Wright.
Representatives of the British and Irish governments, together with local parties - except Sinn Fein - gathered at Stormont yesterday following a month-long summer break. They will go back this morning to discuss the expulsion call.
The loyalist parties are closely associated with the Ulster Volunteer Force and Ulster Defence Association, the illegal paramilitary groups which recently issued death threats against Mr Wright and another loyalist activist. Mr Paisley has argued that the threat breaches the principles of non-violence formulated by the former US Senator George Mitchell, who is chairing the talks.
Mr Paisley said he would take a High Court action if the loyalists were not ordered out.
He said: "How can I debate with these men at the table at the present time? We just can't do it. These parties cannot be associated with such threatened violence for political ends with impunity.
"Failure to distance themselves totally from the murder threat must signal the immediate expulsion of the fringe parties from Stormont. If these parties get away with this threat then the door is wide open for the entry of Sinn Fein-IRA."
In response David Ervine of the Progressive Unionists, the larger of the two fringe parties, said that while the party would not condemn the death threat it was nonetheless committed to the Mitchell principles.
He added: "We have a commitment to the talks, the Mitchell principles and peace within our society. The issue in relation to the threat has absolutely nothing to do with politics. It's a military issue and we have no control over the threat that was made."
The talks, which have yet to deal with difficult issues such as arms de-commissioning and constitution-building, have been re-convened at a time of much pessimism.
This was reflected in an Irish Times poll which reported that only 32 per cent of people thought the talks would succeed, while 63 per cent believed that they would not reach agreement.
The fate of the fringe parties may hinge to some extent on the attitude of David Trimble's Ulster Unionist party, some of whose members appear to favour the expulsion of the loyalists.
The issue is particularly difficult and sensitive. Allowing them to remain, without formally condemning the Wright death threat, would arguably undermine the principle that anyone at the table should not be associated with violence.