The SDLP leader, Mr John Hume, said last night it would be "somewhat tragic" if decommissioning were to become an obstacle to implementing the Belfast Agreement.
Mr Hume said both governments must address the "real issue" and ask whether the paramilitaries had stopped using their weapons and if they were serious in their intention not to return to violence.
Speaking at the European Commission in London, where he was giving the 22nd Thomas Corbishley Memorial Lecture of the Wyndham Place Trust, Mr Hume conceded there were difficulties ahead, "but I hope that we will overcome them".
Mr Hume said that every signatory to the Belfast Agreement and those who would eventually take up office in the government of Northern Ireland must pledge to use peaceful and democratic means to implement the agreement, whose objective was the total disarmament of paramilitary organisations to the satisfaction of the International Commission on decommissioning.
Parties would be automatically excluded from office if they failed to live up to that pledge, he said, adding that such a safeguard would strengthen the position of the Ulster Unionist leader, Mr David Trimble, on decommissioning.
Insisting that the Nobel Peace Prize was an international expression of goodwill towards the peace-makers of Northern Ireland, Mr Hume urged the people of Northern Ireland to "build a trust to erode the distrust of the past" and work to implement the Belfast Agreement, building institutions that respected the differences and healed the wounds of 30 years of conflict.
Speaking earlier in the day in Derry, Mr Hume said the current impasse in the implementation of the cross-Border aspect of the agreement was nothing more than a hiccup.
"Unfortunately there are hiccups at the moment, but we hope we can resolve those."