The Minister for Justice, Mr McDowell, has maintained his verbal offensive on the republican movement by repeating that IRA criminal activity is being used to help fund Sinn Féin.
There were no "Chinese walls" between IRA and Sinn Féin finances, he said yesterday.
Sinn Féin again rejected Mr McDowell's claims, accusing him of "crude posturing", saying he was pursuing an anti-republican agenda and inviting him to produce evidence for his allegations.
Mr McDowell, however, said he was confident that his allegations were correct and that the issue would be raised by the Government during next month's review of the Belfast Agreement. The IRA was engaged in criminality on both sides of the Border, he insisted.
"What I am saying is that the republican movement is single and indivisible at the moment, and that is one of the problems that we have to overcome. There are no Chinese walls between IRA money and Sinn Féin money, and when push comes to shove the resources of one of those organisations is available to the other," he added.
In the House of Commons on Wednesday the British Prime Minister, Mr Tony Blair, also said it was important to make clear during the review that "there cannot be a situation in which a political party is being funded by anything other than purely democratic and peaceful methods".
Mr McDowell said there was "an abundance of evidence that the IRA has engaged consistently in criminal activity to fund the broad purposes of the republican movement.
"There is a difference between producing evidence in public every time you make a statement, and at the same time being confident about the correctness of what you are saying," he told BBC Radio Ulster's Good Morning Ulster programme yesterday.
"For instance, I could say with a considerable degree of confidence that republicans of all hues have been engaged in punishment beatings over the last twelve months. I can say that with confidence even though I can't put my hand on my heart and name the individual who carried out one of those activities," he added.
As for Sinn Féin's rejection of his claims, Mr McDowell said: "I speak on the basis of what I know as Minister for Justice, and am quite confident about what I am saying. I think that some of the people who in public are querying what I am saying in private know in their hearts that I am right.
"We have no doubt that the IRA has on both sides of the Border, and sometimes some quite significant distances from the Border, been engaged in criminal activity. We have to ask the question, what is this money being raised for, what is it being used for, and where is it being put, what are the purposes of the republican movement which requires that such activities should be carried out with a view to financial gain?" he added.
However, Mr Conor Murphy said Mr McDowell was abusing his position to smear Sinn Féin and his comments were prompted by fear of the party's growing electoral strength in the Republic.
The Assembly member for Newry and Armagh said Sinn Féin published its accounts, which were not challenged by the Minister. This further proved the political motivation behind his attack.
"Michael McDowell's crude posturing exposed his real political agenda, his concern about Sinn Féin's increased electoral support and our work in bringing about change in Irish society. Mr McDowell needs to start accepting that Sinn Féin is here to stay," said Mr Murphy.
Mr Ian Paisley jnr said Mr McDowell's comments backed up his party's position that "Sinn Féin/IRA are still immersed in terrorist and criminal activity and are therefore unfit for government".
