The Ulster Unionist Party is to embark on a consultation and clarification exercise after members were "encouraged " by Saturday's IRA statement. The party leader, Mr David Trimble, said it "appears to break new ground".
"I have to say the statement is very interesting; it does appear to break new ground. There are some quite positive elements in it. There are, of course, some questions that it raises and there are points we will want to tease out the meaning of, and we'll also want to get clarification about some of the procedures, particularly on the ways of ensuring that weapons have remained secure," said Mr Trimble.
Speaking outside Parliament Buildings at Stormont after a meeting of the Ulster Unionist Assembly party on Saturday, he said this issue of procedures was "a very important matter", although he described the IRA statement as "promising".
"But we will want to just tease out the meaning before we decide," he added.
No vote was taken at the meeting. However, following consultation with the wider party and clarification on modalities, the matter of whether to re-enter the Executive will go before the Ulster Unionist Council, possibly on May 20th.
Mr Trimble said there were other issues apart from decommissioning which were outstanding. However, he would not confirm if this concerned the retention of the RUC's name.
He said these issues would be discussed "with government" over the next few days "to make sure as much information is in our hands before coming to a conclusion.
"We want to see this process succeed. We want to see it built on solid, secure foundations. We will be anxious to ensure that those foundations are there and we will be considering matters further."
Yesterday, Mr Trimble said the party would have to explore exactly what was meant by an inspection process; how it was going to be conducted; and what procedures would be adopted to ensure weapons remained secure.
"And then we want to be sure that this process of inspection is part of an overall process leading to full and complete decommissioning, and that when the IRA say they will put their guns beyond use completely and verifiably, that it is complete, that it is permanent," he said.
The Ulster Unionist Party security spokesman, Mr Ken Maginnis, said: "There does appear to be potentially enough there for something to be worked out. We've certainly indicated we are interested and encouraged in principle but the devil is in the detail.
"It looks promising but much will depend on how it is implemented, particularly in respect of practical and technical details.
"That said, it's definitely a move from the `not a single bullet' position and we'll be making an effort to see it's properly built on. Suspicious unionism will be frustrated but unionists are not, by and large, unreasonable," he said.
Mr David McClarty, the Assembly member for East Derry, said the IRA statement, distributed just before the meeting of Assembly members, had led to "a great deal of encouragement among members".