Sinn Féin has said it is time for the Minister for Justice to "calm down" after he again attacked republicans in a speech delivered to the Progressive Democrats in Dublin today.
Mr McDowell said the Provisional movement had "stolen and abused the language of republicanism to justify a savage, anti-democratic, crime-ridden, and shameful campaign" that "does violence" to the 1916 Proclamation.
He also said the time has come for "genuine republicans" to reclaim the language of their beliefs from "those who have hijacked and perverted it for base, discredited, destructive and shameful ends".
Although he did not name senior Sinn Féin figures, the Minister said "no true republican" would "lie and lie again" about his involvement in violence. Mr McDowell earlier this week said senior Sinn Fein figures were members of the IRA Army Council, a statement denied emphatically by that party.
Mr McDowell said his recent remarks concerning the activities of the Provisional movement have been criticised by that movement as "anti-republican" and that he could not "allow that further usurpation of the language of republicanism to go unchallenged".
"Republicanism does not speak in muffled voice through a balaclava; Republicans don't break drug-addicts' legs with baseball bats; Republicans do not finance their political campaigns by organising major crimes: Republicans do not shoot car-thieves in their knees and ankles: Republicans could not plant bombs to kill civilians at Enniskillen, Omagh, the La Mon hotel, or Manchester, Birmingham and Canary Wharf.
"No true republican could have looked through binoculars at the children on a boat at Mullaghmore before deliberately blowing them to pieces. And no true republican could publicly lie and lie again about his involvement with all of those matters."
"The truth is that the Provisionals are the embodiment of all that is anti-Republican. Their ideology, methods, and values would have disgusted the founders of our State," Mr McDowell said.
Responding to the remarks, Sinn Féin's spokesman on justice, equality and human rights Mr Aengus Ó Snodaigh said this evening: "It is time for Justice Minister Michael McDowell to calm down."
"Earlier this week Sinn Féin President Gerry Adams called for an end to the frenzy of spin and invective and for a calm debate on these and other matters. But instead Michael McDowell has engaged in another vicious attack on our party.
"We certainly need a full debate on the future of Irish republicanism but today's tirade of abuse will do little other than keep the minister in the headlines.
"In relation to today's comments, republicanism is not owned by any party. It is a political philosophy which many people support in different forms.
"The republicanism which Sinn Féin stands for is the exact opposite of that of Mr McDowell's and the PDs'. He would see undone the rights and equalities people have won after many years of campaigning. We in Sinn Féin are, and have been for years, embracing equality and trying to build an equal society in Ireland."
"A look at Mr. McDowell's record makes his position clear - negative on rights for immigrants, on rights for travellers, on rights for prisoners, on rights for refugees and even reluctant to formulate a proper Immigration policy. I would say that his values are the antithesis of those values enshrined in the 1916 Proclamation - a Constitution that he would envisage would not cherish all the children of the nation when he wants to deny citizenship to those born here."
Mr Ó Snodaigh said it was very important to "keep an eye on the bigger picture", which he did not think the minister did and "certainly not" with the peace process in Northern Ireland.
"I wonder if we would have gotten as far as the Good Friday Agreement if he were Minister for Justice
at the time. He was one of the most ardent critics, in the early 1990s, when John Hume was engaging in talks with Gerry Adams, which launched the peace process.
"I am all in favour of discussing Irish republicanism but I think it would be better conducted in a calm atmosphere."