A statement from "Real IRA" members in Portlaoise jail said the current army leadership had forfeited all moral authority to lead the (Real) IRA.
The "Real IRA" also referred in a separate briefing document to the deaths in the Omagh explosion, saying they had irreparably "damaged" the Irish Republican struggle.
It said the attack had been launched with the Continuity IRA fellow terrorist faction. It also confirmed the "Real IRA" involvement in the Omagh bombing in 1998, when 29 people were killed and another 200 were injured.
The statement published in the Sunday Independent said:
"On Friday, September 27, in a written communication to the Army leadership, the (Real) IRA unit in Portlaoise Prison took the unprecedented step of calling the Army Council to stand down with ignominy.
"We will not demean our struggle or provide succour to our enemies by revealing the comprehensive catalogue of evidence which has exposed this leadership.
"However, we do feel duty-bound to state that this Army leadership's financial motivations far outweigh their political commitment to our struggle at this time.
"IRA prisoners find this morally and politically unacceptable. We believe that the current Army leadership has forfeited all moral authority to lead the (Real) IRA.
"To date, the leadership has failed to respond to our demand.
"Thus we feel we are left with no option but to withdraw our allegiance from this Army leadership.
"We would like to take this opportunity to reaffirm our commitment to republican principles and reiterate our steadfast opposition to the Belfast Agreement and British rule in Ireland.
"Furthermore, in order to dispel recent, mischievous leaks to the media, we would like to state that no IRA prisoners' representative has entered negotiations with any government regarding the early release of political prisoners."
The statement is signed: "IRA unit, Portlaoise."
Mr Michael Gallagher, whose son died in the Omagh bombing, said it was "great news" but he wanted to know at what price the disbandment had been achieved. "We are aware that the Irish Government have been in talks with the "Real IRA" for some considerable time," he said.
"The Irish Government must come clean about how this was brought about and what concessions and incentives were given.
"Is this going to affect the search for the Omagh bombers?"