The Progressive Unionist Party leader, Mr Hugh Smyth, has said that Sinn Fein could help to end the political stalemate by clearly stating that the Provisional IRA's war is over.
Mr Smyth, a former lord mayor of Belfast, told his party's annual conference that Sinn Fein had a responsibility to allay unionist fears about its entry into an executive.
"I say to the republican movement, I say to Gerry Adams, that if you have difficulty with decommissioning, as we recognise, then fine. Do something more.
"I want the republican movement to tell me and my people, the unionist people, that the war is over.
"Let them match what the loyalist paramilitaries have said and tell us there won't be a first strike from them. If Sinn Fein states clearly there will be no first strike from them, the loyalist paramilitaries have already stated there will be no first strike from them.
"You don't need to be a genius to work out the situation from there."
A similar plea to republicans was made by Progressive Unionist Assembly member Mr Billy Hutchinson, who acts as an interlocutor for the UVF and the Red Hand Commando with the international decommissioning body.
He said the silence of the Provisional IRA was perceived by unionists as "some sort of threat". He stated: "The UVF have been clear in trying to send out positive messages to society as a whole, I am sure there are statements that could be made that would clearly show the IRA's intentions in the process.
"The unionist community are the British presence and you're going to have to deal with them one way or the other, politically or militarily. You either want to break the impasse or you don't.
"Loyalists would be interested in hearing if the agreement is the basis on which this conflict can be settled or why you feel there is nothing you can say or do to convince the British community that you are genuine in your search for peace."
Mr Hutchinson said that demands for loyalist paramilitaries to "take the high moral ground and decommission first" were not realistic.
The loyalist ceasefire was five years old and should not be forgotten. He criticised the Ulster Unionist leader, Mr David Trimble, for not recognising the vital role played in the peace process by mainstream loyalist paramilitaries.
"My message to David Trimble is a simple one. Remember the contribution of loyalists to a peaceful and progressive way forward should never be underestimated.
"The foundations of the peace and political process have been mooted by loyalists long before mainstream unionists and nationalists could even dream of an inclusive society.
"What we must do now is to stay on the right track and continue to engage each other, creating the space for others to move - not lambast each other in the media."
A PUP delegate, Ms Dawn Purvis, told the conference that the militant anti-abortion and anti-contraception group Precious Life represented a grave threat to fundamental freedoms.
"Everyone is entitled to their opinion but what gives them the right to behave in such a way that young women seeking information from a family planning association are so frightened to pass the Precious Life picket that they don't enter the building but ring the clinic from a phone box down the street?"