This is to be done by the introduction of a procedural motion, the terms of which were being worked on overnight, which would effectively herald the start of real negotiations.
Yesterday's session was described as historic in that it brought Ulster Unionist and republican leaders together in the same room for the first time in generations. Next week promises to be even more significant if the two sides begin to do business, even if only at a distance.
The Unionist party brought forward an indictment against Sinn Fein, seeking to have the republicans expelled from Stormont. This took the form of a 30-minute attack by the party's security spokesman, Ken Maginnis MP.
Mr Maginnis and his party leader, David Trimble, then left the room before Sinn Fein's president, Gerry Adams, made his reply, though other Unionists stayed behind.
According to a number of sources Mr Adams's reply was made in generalised terms, taking up less than 10 minutes.
One person who was present said: "It was not a very sharp Unionist attack. It was a piece of cake for Adams to deal with it - he just took the high road, said he wanted to look forward, stretch out the hand of peace, and so on."
Various other parties contributed to the discussion, but the session lasted only 90 minutes rather than the three hours which had been set aside for it. The British government is to give its ruling on the indictment today, but it is considered a foregone conclusion that Sinn Fein will not be ejected from Stormont.
The Unionist party has made it clear that it will remain in the talks even if, as expected, Sinn Fein are not thrown out, though Mr Trimble said the party would vary its tactics on a day-to-day basis.
One participant described the session as a damp squib, while another said the Unionist attack must have been like "being beaten with a stick of celery." The middle of the road Alliance Party said the occasion had been "like a boxing match where one of opponents had attacked the referee and the crowd but had not laid a glove on his opponent".
The Government will be happy that the occasion has passed without real fireworks and that it appeared to assume an element of ritual rather than posing any obvious danger to the continuation of talks.
Outside the talks Mr Maginnis continued the attack on Sinn Fein, declaring: "The truth will come out about Sinn Fein and the IRA and the Secretary of State had better guard her language very carefully in how she responds to the charges we put today. She had better be careful what she says in case her words turn round and bite her.
"We know that Martin McGuinness and Gerry Adams have been actively involved in the IRA's terrorist campaign since the beginning as activists, as commanders and now as godfathers. Let them deny what everyone knows and make greater liars of themselves than they already are."
Emerging from the talks, Mr Adams dismissed the Unionist indictment as a sham, declaring: "This was hailed as the great confrontation, the great showdown, the great challenge to Sinn Fein. But the leaders of Unionism came into the room, made a submission and then scampered out of the room to talk to the media.
"David Trimble didn't say anything and had he listened to what I had to say, I made the point that every section of our people have suffered and that none of us have a monopoly on suffering."
Mr Trimble was attacked by the Rev Ian Paisley's Democratic Unionist Party for taking part in the talks process. Peter Robinson MP said: "Today's sham fight at Stormont is but the slip road to full negotiations between the Ulster Unionists and the IRA.
"Trimble and company have ditched every commitment they gave and every principle they held. Boy David may come out beating his chest, but in reality he is beating a retreat."
British and Irish government ministers met last night to plan the next move in the talks.
Mr Trimble was seeking to remodel the talks process.
"There will be other ways and other opportunities for us to put Sinn Fein on the back foot. We will pick and choose what we do and our tactics.
"We are there not to negotiate with Sinn Fein and there is no obligation for us to be present the whole time. We will negotiate with the Government and other parties. We can pick and choose bilaterals," he said.Reuse content