The IRA's "Army Council" still exists, an independent review of paramilitary activity has said, however in a "much reduced form".
Northern Ireland Secretary Theresa Villiers told Parliament that all the loyalist and republican groups that declared ceasefires during the peace process in the 1990s have gone on to commit murder in the years since.
But she said none were currently planning or conducting terror attacks.
She added that some individual IRA members remain involved in criminal activity, such as large scale smuggling.
Outlining the findings of the review, Ms Villiers said: "On the purpose of these groups the report concludes that 'it is our firm assessment that the leaderships of the main paramilitary groups are committed to peaceful means to achieve their political objectives' but that 'we judge that individual members of paramilitary groups with a legacy of violent activity still represent a threat to national security'."
Sinn Fein's Martin McGuinness gives his reaction in the wake of the publication of a Government-ordered review of paramilitary structures in Northern Ireland
The assessment, which was prompted by an IRA-linked murder in Belfast in August, examined the structures of groups including the Provisional IRA, the Ulster Volunteer Force, Red Hand Commando, Ulster Defence Association and Irish National Liberation Army.
The murder of ex-IRA man Kevin McGuigan, 53, had thrown Stormont's power-sharing executive into disarray, with all but one of its unionist ministers having walked out, claiming trust in Sinn Fein has been shattered.
Ms Villiers said: "On structures the assessment says that 'the majority of paramilitary organisations in this report still have leadership structures' and 'organise themselves along militaristic lines'.
"It goes on to say that 'these labels make the groups look more prepared for a campaign of violence than they are' and that 'in the highly unlikely event that the groups were minded to return to terrorism, we judge they would be unable to resurrect the capability demonstrated at their peak'."
The report found that while the majority of paramilitary weapons have been decommissioned, "some were not".
Ms Villiers said members of the paramilitary groups were engaged in serious criminal activities for "personal gain", including large scale smuggling operations, fuel laundering, drug dealing and extortion.
In regard to the Provisional IRA, the assessment found that "the structures of PIRA remain in existence in a much reduced form".
These structures include "a senior leadership, the 'Provisional Army Council' and some 'departments'," the report said.
Ms Villiers told MPs that the independent panel did not think the IRA was actively recruiting or rearming.
The Northern Ireland secretary added: "I will not seek to hide from the House that much of this assessment makes uncomfortable reading.
"These organisations should never have existed in the first place and 21 years after the first ceasefires and 17 years after the Belfast Agreement it is clearly unacceptable that they still exist today.
"For all that the assessment judges the leaderships of the main paramilitary groups to be committed to peaceful means, such groupings have no place in a democratic society.
"Members of these groups continue to exert a malign influence which as the assessment puts it 'harms communities and damages the financial prosperity and reputation of Northern Ireland'.
"Inevitably an assessment of this kind does not provide all the answers but I hope it will assist in identifying the nature and scale of the problem and framing the debate about the way forward."
The report stated that IRA members believe the Army Council "oversees both PIRA and Sinn Fein with an overarching strategy".
However it said this strategy has a "wholly political focus".
The report said:
"The PIRA of the Troubles era is well beyond recall.
"It is our firm assessment that PIRA's leadership remains committed to the peace process and its aim of achieving a united Ireland by political means.
"The group is not involved in targeting or conducting terrorist attacks against the state".
Since the crisis sparked by the McGuigan murder, the Stormont administration has limped on, with many departments shorn of continuous ministerial leadership, while crisis political talks involving the five main parties and the British and Irish governments have tried to find resolution.
But the negotiations have effectively been in a holding pattern pending the outcome of the review of paramilitarism, which was based on assessments by the Police Service of Northern Ireland (PSNI) and MI5.
The three members of the panel asked to conduct the exercise were former independent reviewer of UK terror laws Lord Carlile of Berriew; Rosalie Flanagan, a former permanent secretary at Stormont's Department of Culture, Arts and Leisure; and Northern Ireland-based QC Stephen Shaw.
Mr McGuigan was shot dead in Belfast in August in a suspected revenge attack for the murder of former IRA commander Gerard "Jock" Davison, 47, three months earlier.
Detectives believe some of Mr Davison's associates suspected Mr McGuigan of involvement in his shooting.
Before the McGuigan murder, the future viability of the administration had already been in doubt as a consequence of long-standing budgetary disputes, with the row over the non-implementation of the UK Government's welfare reforms the most vexed.