UUP deputy leader Danny Kennedy has accused the de Chastelain commission of failing to maximise public and unionist confidence in the scrapping of IRA weapons.
"There was a failure to do that," he said. "We made that point very strongly to the general and his colleagues. But to in some way implicate or blame the independent witnesses and accuse them of a lack of integrity is misplaced and wrong."
Mr Kennedy said he put to the decommissioning body a number of questions but failed to receive "full replies" because of the confidential nature of the IRA's relationship with Gen de Chastelain and his two colleagues.
"We have criticism in that regard. However, we are satisfied and accept that a significant act of IRA decommissioning has taken place and I think other political representatives have, in their own way, accepted that principle too. We now move on to assess how wedded to democratic politics will Sinn Féin and the republican movement become as a consequence."
Mr Kennedy added: "We are given to understand by IICD officials that republican decommissioning on behalf of the Provisional IRA is now complete. Those who want a photograph will not get it - we were always more interested in product. We retain scepticism on the basis that it [ decommissioning] wasn't done more publicly or as fully or as transparently as we would have liked. But it appears that the issue has been dealt with and we now move on to assess how the republican community will react in terms of their politics and, more importantly, the criminality aspects of their organisation."
Mr Kennedy warned against putting too much store on the contents of future reports by the Independent Monitoring Commission expected next month and in January, when the two governments are expected to push for the restoration of the assembly.
"We will continue to monitor closely the activities of republicans on the ground," he said. "When we get IMC reports we will set them against other reports."
Referring to DUP criticisms of Fr Alec Reid and the Rev Harold Good, Mr Kennedy said he had known Rev Good for many years as a man of the utmost integrity.
"He started his ministry in my home village of Bessbrook [ Co Armagh]. He is a well-respected church figure within his own tradition of Methodism and also within the wider church family. He has exercised a valuable ministry in terms of mediation.
"Under no circumstances would I question or would my party question the integrity or honesty of the Rev Harold Good."
Mr Kennedy added: "However, I would have to say also that it remains a matter of regret that others from another Christian tradition have chosen to do so."
The Ulster Unionists are to meet the two clerical independent witnesses later this week.
The Rev Ken Newell, a former Moderator of the Presbyterian Church in Ireland, said what were required of any independent witnesses were "total independence and integrity".
He added what was also required was the capacity "to wreck any kind of deception".
"Alec Reid and Harold Good are those kind of men," he said.
Alliance leader David Ford said after his delegation's meeting with the IICD that the British government must avoid making what he called "knee-jerk concessions" to republicans on the back of IRA decommissioning.
"The political process must be more than simply the British government trading concessions for IRA decommissioning in order to safeguard their own narrow security interests," said Mr Ford.