The IRA is no longer involved in any centrally organised criminality, the British and Irish governments believe.
The IRA announced an end to its armed campaign in July 2005
Speaking after meeting Irish ministers, NI Secretary Peter Hain said cross-border intelligence indicated the IRA was living up to its commitments.
Mr Hain said individual IRA members may still be involved in criminal activities, but that should not prevent political progress from being made.
However, the DUP's Nigel Dodds said Mr Hain was "living in fantasy land".
"This latest assessment from the secretary of state lacks credibility and will be treated by the vast majority of people in NI as yet another ham-fisted attempt to bluff the community and its political representatives into establishing an executive including Sinn Fein."
He added: "These comments that the IRA is not engaged in criminality fly in the face of the recent Northern Ireland Select Affairs Committee report on organised crime."
Mr Hain said that an "absolute state of perfection" from the IRA was not realistic.
"There probably is still some localised individual criminality by former and maybe existing Provisional IRA members for their own private gain," he said.
"What there is not is organised 'from the centre' criminality any more."
"To that extent the IRA are delivering on their commitments made last July, not just in respect of shutting down paramilitary activity but also shutting down criminality."
Mr Hain was speaking after meeting Irish government ministers Dermot Ahern and Michael McDowell in Hillsborough, County Down.
Irish Justice Minister Mr McDowell, who has been strongly critical of republicans in the past, backed Mr Hain's assessment.
Asked if he believed the IRA's war was now over following its declarations and decommissioning last summer, he said: "The Irish government and British government are working on that assumption, based on the evidence we have."
BBC Northern Ireland political editor Mark Devenport said it was as firm a statement on IRA criminality as the two governments had made since it announced in July 2005 it was ending its armed campaign.
Alliance Party leader David Ford said the statement was "unhelpful".
"We have suffered in the past, when ministers have acted as cheerleaders for paramilitary organisations, and made positive comments when they have not been justified," he said.
"He needs to leave such statements to the IMC, as it is their role, and their role only, to report on paramilitary criminality."
Peter Hain met Irish government ministers at Hillsborough
The DUP are demanding more proof that the IRA has abandoned all violence and criminality before re-entering any power-sharing executive with Sinn Fein.
Devolved government was suspended over allegations of a republican spy ring.
The court case that followed collapsed and one of those involved, Denis Donaldson, later admitted working as a British agent. Direct rule from London was restored in October 2002 and has been in place since.
The British and Irish governments have given Northern Ireland's parties until 24 November to reach agreement on restoring devolution.