The IRA leadership is committed to "following a political and peaceful path", according to the body set up to monitor paramilitary activity.
The assessment of the IRA was given by the IMC
The Independent Monitoring Commission found the IRA had reduced its criminal activity and intelligence gathering.
However, it said some senior members were still involved in crime and some weapons had been retained by local IRA units in defiance of the leadership.
Prime Minister Tony Blair said the report was an "important step forward".
"The fact that it is a positive report leads us to be more hopeful and optimistic that we can get to a situation where the confidence exists for the institutions to get back up and running," Mr Blair said.
"There is a framework, everyone knows what it is, so my plea to everybody engaged in this is 'get involved'."
In its tenth report on Wednesday, the commision said the IRA leadership was "working to bring the whole organisation fully along with it and has expended considerable effort to refocus the movement in support of its objective.
"In the last three months this process has involved the further dismantling of PIRA as a military structure," it said.
"We have had no indications in the last three months of training, engineering activity, recent recruitment or targeting for the purposes of attack.
"There has now been a substantial erosion in the PIRA's capacity to return to a military campaign without a significant period of build-up, which in any event we do not believe they have any intentions of doing."
It also warned that republican dissidents and loyalist paramilitaries were continuing to recruit and attempting to acquire weapons, and remained a threat.
Joe Brosnan of the Independent Monitoring Commission (IMC) said it was the "most positive report we have done, so far, on the IRA".
Northern Ireland Secretary Peter Hain said: "The government believes that it should make a helpful contribution to the rebuilding of trust and confidence in Northern Ireland which is necessary for a return to full devolution."
He told the House of Commons the report had to be viewed in the context of the "historic change" that had been seen.
The IMC monitors paramilitary activity
Martin McGuinness of Sinn Fein said the IRA had "addressed unionist concerns and removed any further excuse for non-engagement".
He added: "The DUP must now decide if they want to come on board the peace process and see the re-establishment of the political institutions in the immediate time ahead."
DUP leader Ian Paisley said that a full statement was needed of what the IRA had decommissioned.
"The policy of the united voice of the unionist people insisting that criminality must cease is taking effect and we welcome the effect it is taking," he said.
Ulster Unionist leader Sir Reg Emey said the report "continues to represent progress".
"However, the dog that didn't bark is the IRA authorised Northern Bank robbery and the failure of republicans to return the money. The UUP calls for an immediate return of these funds."
SDLP leader Mark Durkan welcomed progress on IRA activity but urged the government and the DUP to give a stronger message to loyalist paramilitaries.
"Instead of throwing them concessions, the British Government must give loyalist paramilitaries the clear message that they must wind up or be shut down. The DUP must be equally clear on this," he said.
Alliance leader David Ford welcomed the report and said it showed progress was being made to end violence and criminality by mainstream republicans.
"We welcome the reduction in criminality. We also welcome the positive effects that the IMC is having on the process to restore local democracy," he said.
Irish Justice Minister Michael McDowell said the report was "both welcome and timely given the efforts being made to restore devolved government in the province".
He said: "The developments outlined in the report help to create the proper environment in which the political parties can come together on 15 May next and begin the process of self-government."
The Independent Monitoring Commission was set up by the British and Irish governments in January 2004.
It also monitors the "normalisation" of security measures in Northern Ireland.
Its four commissioners come from Northern Ireland, the Republic of Ireland, Britain and the US.