The Minister for Justice has challenged Sinn Féin to deny it owes a deeper loyalty to a "mythological view of Irish history than to the democratic organs of the State".
Mr McDowell said this mythological view of the Provisional movement, which included the IRA and Sinn Féin, was that its members "and a few people who are unknown to the great majority of Irish people, carry within them a moral legitimacy and mandate which is superior to the laws and Constitution of this State and any agreements made by the Irish people".
In a swingeing attack on the party, he said they were not the representatives of republican opinion in the Dáil.
He was speaking during the first Dáil debate on the Independent Monitoring Commission Bill, establishing the body that will monitor any breaches of the Belfast Agreement.
Sinn Féin has rejected the Bill as a breach of the agreement and the party's Dáil leader, Mr Caoimghín Ó Caoláin, dismissed the Minister's "moralising and lofty lecturing".
Mr Ó Caoláin denied the Minister's claim that he was telling "untruths", and "time will tell which of us was reflecting on the factual interpretation and understanding of what is involved in this Bill before us".
Sinn Féin members "are democrats and we are committed to the sovereignty of the people and to the democratic institutions established by them".
Mr McDowell said if Mr Ó Caolain believed the Bill was in breach of the agreement, "let he and his colleagues go to the Four Courts and make that case before the independent judiciary of the State". The Government was acting in support of the agreement and to ensure it prospered. The "time has come and gone for some people to resile from moral ambiguity, ambivalent language and the practice of speaking from both sides of their mouths on where legitimacy resides in this State and in Northern Ireland".
The Provisional movement comprises people who "constantly mask one truth about themselves. Far from regarding the institutions and Constitution of this State as legitimate, they state, on the contrary, that the Army Council of the IRA, the executive of that body and the convention, which is another attribute of IRA organisation, have democratic legitimacy and enjoy a continuous thread of legitimacy that dates back to the 1918 general election." It "carries the implication that such legitimacy is denied to this Parliament, the will of the people in this State and the Constitution".
He said it was that "fundamental moral ambiguity, writ large and infecting a series of issues, that has bedevilled progress on this island in implementing the agreement. It is this incapacity to deal fairly and squarely with the issue that has brought lack of trust and ill-feeling to the centre of Northern politics." He did not claim that all the blame lay with the Provisionals "but it is a significant portion. They have short-changed everybody else in the process because of the fundamental intellectual and moral contradictions at the centre of their movement."