The Ulster Unionist leader has reacted positively to elements of a speech made by Mr Gerry Adams on the future of the peace process and the continuation of paramilitary groups.
Mr David Trimble said yesterday he believed Sinn Féin "was in the market" for discussions on a political way forward.
"The significant thing is, he never said never. We didn't get any echo of the sort of language that came from republicans on decommissioning in 1998-99. You could take from what he said on Saturday as part of the business of conditioning members of the IRA, to make them realise that yes, they are going to go away."
He added however that Mr Adams was speaking for Sinn Féin.
"We'll only know they're really serious when we hear things from the IRA as well."The agreement set out very clearly the objective of the complete disarmament of all paramilitary groups and people committed themselves and had obligations towards that.
"The agreement also makes absolute the commitment to exclusively peaceful and democratic means and that means no private armies. \ does not say explicitly that there must be abolition of private armies but that is clearly the meaning of the agreement."
Mr Trimble said he envisaged a future back in the Executive alongside Sinn Féin "if the paramilitary issue is resolved". He said this meant a situation where everyone knew there were "no private armies and that people are committed to exclusively peaceful and democratic means".
He insisted other groups, not just the IRA, needed "sorting out". He referred to "acts of completion" and said Ulster Unionists would not return to the Executive table with Sinn Féin "on the basis of some promises or mere beginnings".
The British Prime Minister, Mr Tony Blair, referred to "acts of completion" in his address in Belfast on October 17th. He promised swift and complete fulfilment of the Belfast Agreement should paramilitary activity cease.
In his address to Sinn Féin elected representatives at the weekend, Mr Adams also used the phrase. "He [Mr Blair] said that the time for transition had come to an end. There was a need for acts of completion. Again, I agree."
Mr Trimble cast doubt on the possibility of Assembly elections being held on May 1st next year, as timetabled.
Mr Trimble asked: "How can you possibly have an election to something that's suspended?"