The 32 County Sovereignty Movement has said grassroots republicans on both sides of the Border must seriously consider their allegiances following the Provisional IRA's action on decommissioning.
Mr Rory Dougan of the Sovereignty Movement said: "By no stretch of the imagination have acts carried out by the Provisional leadership in the past 24 hours any place in a republican strategy.
"It is unprecedented in Irish history for a revolutionary army to surrender its weaponry."
Security sources say the Sovereignty Movement is the "Real IRA's" political wing, a claim the group denies.
Mr Dougan said it was now impossible to differentiate Sinn FΘin's politics from those of Fianna Fβil.
"There has been a complete metamorphosis from a revolutionary movement into a partitionist, constitutional political party.
"Gerry Adams has admitted this is a leadership-driven strategy.
"Republican grassroots had virtually no say. It is now time for that grassroots to seriously consider whether their allegiance is to one particular political party or to the goal of a 32 county sovereign Ireland."
Republican Sinn FΘin ard comhairle member, Ms Geraldine Taylor, said world history showed it was only "defeated armies" which surrendered their weapons.
"The Provos had no right to decommission. Those weapons were bought to free Ireland and men and women fought and died to acquire them.
"If the Provos were no longer willing to continue the struggle, then they should have handed the weapons on to those people who are still prepared to do so.
"Instead they have surrendered arms at the behest of the British establishment," she said.
Security sources say Republican Sinn FΘin is the political wing of the Continuity IRA, a claim the party denies.
The Republican Sinn FΘin president, Mr Ruair∅ ╙ Brβdaigh, said: "Cumann na nGaedheal/Fine Gael, Fianna Fβil, and the Workers' Party did certainly betray republican principles and accept British rule in Ireland.
"But none of them ever stooped to destroying weapons given to them to achieve Irish national independence."
Both "Real" and Continuity IRA sources claim there is considerable dissatisfaction among republican grassroots at the action on decommissioning.
"Gerry Adams's constant references in his speech to the need for unity in the ranks shows he is very worried about the situation," said a "Real IRA" source.
Security sources predict there will be defections from the Provisional IRA to both dissident groups in Belfast, Derry, and Border areas.