The Sinn Féin president, Mr Gerry Adams, has accused the Minister for Justice, Mr McDowell, of abusing his position to make "malicious claims" about Sinn Féin's finances in an attempt to halt the party's electoral rise.
In a statement yesterday after his party published its 2002 accounts, Mr Adams said Mr McDowell's allegations that Sinn Féin had "deep and ongoing links to criminality" had no substance.
The charges "go beyond the normal cut and thrust of acceptable political comment, not least because Michael McDowell is speaking in his capacity as Minister for Justice".
Mr McDowell said recently that Sinn Féin was "morally unclean", and suggested it was funded by the proceeds of IRA criminal activity.
Mr Adams said yesterday that the Minister knew Sinn Féin's accounts were properly audited, and adhered to all the guidelines set out North and South in relation to fundraising and spending.
"Minister McDowell's attacks are really about his concern about Sinn Féin's increased electoral support, and our work in bringing about change in Irish society.
"I have no doubt that Minister McDowell will pay little heed to any request from me for him to put up or shut up. He is serving a political agenda which has little affinity with republicanism or nationalism. But others in the Government who do represent republican and nationalist constituents are appalled by Minister McDowell's behaviour."
He said Mr McDowell had spoken out against the Hume/Adams talks and the peace process in the early 1990s, and these latest remarks "will have as little impact".
A party spokeswoman said the party was taking legal advice in relation to some of the claims about Sinn Féin funding that had been made in the media in recent weeks.