The Minister for Justice, Mr McDowell, said he knows the links between senior Sinn Féin figures and the IRA - but he doesn't want to be accused of "wrecking" the peace process.
Mr McDowell declared that senior figures in Sinn Féin were "certain members" of the IRA Army Council and that "there was no point in pretending otherwise".
He said he knew who the members of the Army Council were, but as a member of government he has decided not to reveal them in the hope that the IRA will disband.
But when challenged to name the members by Sinn Féin MEP Mary Lou McDonald, Mr McDowell said: "If you really did want me to name them, you would then accuse me of trying to wreck the peace process."
Speaking on Today FM's Sunday Supplementradio programme today, Mr McDowell also said that the Army Council "determines where the Republican movement goes".
Ms McDonald countered: "I have no balaclava. Sinn Féin is a democratic party and we are part of the political mainstream. Sinn Féin is no safe haven for criminality."