Dáil deputies have approved a motion calling on republicans to end criminality and paramilitarism and to commit to decommissioning.
The measure was backed by all the main parties, however, Sinn Féin claimed they were being attacked by people who had always been opposed to the peace process.
During the debate, the Justice Minister said that attempts to reach a deal in Northern Ireland were blocked by Sinn Féin’s refusal to sign up to a proposition against the endangerment of human rights.
Michael McDowell told TDs that opposition to the use of violence was as central to the Good Friday Agreement as any electoral mandate secured by any party.
The minister said the issue of criminality would not go away for republicans, and when that was understood, there might be a chink of light on the efforts to reach a deal in Northern Ireland.
Mr McDowell also said that punishment beatings had been turned on ‘as if by a click of the fingers’ by the republican movement.
He accused the provisional IRA of engaging in criminal activity on both sides of the border since 1998, moderated from time to suit their political ends.
Mr McDowell said that the Dublin brigade of the IRA had been stood down, after it had been found to have pilfered money raised for the republican movement.
He added that criminal activity in the south had then been overseen by the IRA Adjutant in Belfast.
The Green Party leader, Trevor Sargent, said Sinn Féin needed to move on and to reflect on its role in relation to policing.
Sinn Féin TD Caoimhghin Ó Caolain rejected what he said were false accusations of criminality that had been made against republicans.
The deputy said Sinn Féin rejected criminality of every kind. But he believed the false charges were not about the peace process, but about party politics.
He said all the old opponents of the peace process had come out of the woodwork and he included Mr McDowell in that group.
Deputy Ó Caolain urged the British and Irish governments to implement aspects of the Good Friday Agreement, including demilitarisation, police reform in North Ireland and increased co-operation between north and south.