The guarantees offered about the IRA's destruction of arms by Gen John de Chastelain and two independent church witnesses should be believed, the SDLP has said.
Following a meeting with the Independent International Commission on Decommissioning (IICD), Alex Atwood said they were "more reassured".
The IICD had made it "very clear to the IRA that the IRA had to be absolutely true and honest" about its decommissioning intentions, or never be believed again.
Rejecting Democratic Unionist Party charges against the IICD and the church witnesses, Mr Atwood said they were "in nobody's pocket, or nobody's fools.
"They said to the IRA that the IRA could only get this right once and if they got it wrong, if the IRA were not being upfront, straight and true then that would become clear," he told journalists.
However, the IRA must face major penalties if it ever goes back to violence, he said. "If in the future the IRA uses a gun, or robs a bank, or threatens a family then everybody including governments must call it.
"Yesterday should have been the end of ambiguity. In future there must be no ambiguity from the governments. The nature of the process must change," he warned.
Dismissing the DUP's criticisms that former Methodist president the Rev Harold Good and Redemptorist priest Fr Alec Reid were "IRA appointees", Mr Atwood said: "People have to see beyond the issue of who did or didn't appoint the witnesses.
"The real issue is: do people believe that the three members of the commission and the two witnesses are in somebody's pocket, or are fools? Do people seriously conclude that they are either one or the other?" But he warned that the DUP would not be prompted by the IRA's move into a speedy return of the Northern political institutions.
The DUP's opposition to such a move was not a posture.
"You can conclude that it is hardening, both a tactical and a strategic hardening," Mr Attwood said. However, many in the Unionist community, "including those who have suffered horribly" were quite clear that "a massive act of decommissioning" had taken place.
"If unionism across its broad range is recognising that this is different, then it is difficult for the DUP to sustain the argument that things are worse than they were before. That is a problem that they will have to get their head around," he told The Irish Times.
Speaking from Brighton, SDLP leader Mark Durkan said the Irish and British governments should prevent the DUP from blocking progress .
"The Ulster Unionists played the delay game by blocking the setting up of the Executive. Then Sinn Féin played the same game over decommissioning. Now the DUP thinks its their turn.
"The governments have to be rock-solid in their response. They should tell the DUP where to go, back into the Good Friday agreement's institutions." The DUP, he said, was trying to "turn the clock back on change".
"They must not succeed with this destructive agenda. The governments must stand firm for 50-50 [ police] recruitment, protect the Parades Commission.
"They must not fall into the trap of delivering side deals to the DUP. The culture of side deals has only damaged the political process and taken us all away from the Good Friday agreement," he said.