Sinn Féin chief negotiator Mr Martin McGuinness has repeated his denial of the claim made by the Minister for Justice, Mr McDowell, that he is a member of the IRA's army council.
In an interview on Today FM yesterday, Mr McDowell claimed Sinn Féin president Mr Gerry Adams, as well as Mr McGuinness, and Kerry South TD Mr Martin Ferris, were members of the IRA leadership.
Sinn Féin's chief negotiator, Mr Martin McGuinness
Speaking on this morning's BBC Radio 4 Todayprogramme, Mr McGuinness said: "No I am not. I deny that. I reject that absolutely.
"Michael McDowell, right throughout the course of his political career, has been hostile to Sinn Fein, to Irish republicanism. . . . Clearly . . . this is about electoralism, this is about his concern about the growth of the Sinn Féin vote."
Mr McGuinness was asked whether he would regard it as a crime if the IRA was involved in punishment beatings or a murder.
He said: "I am opposed to all criminality, no matter who is involved. . . . I have been hostile to punishment beatings and criminality of all descriptions for my entire political life.
"I believe that anyone who is involved in punishment beatings or shootings was involved in criminality."
Mr McGuinness said he wanted anyone with information about the murder of Belfast man Robert McCartney to make it known.
The IRA has faced claims that it has sought to protect the killer and intimidate witnesses.
Mr McGuinness said: "We have said very very clearly from within Sinn Féin that anyone who has information about that should not hold that information back, should bring it forward, and there are different avenues that people can use.
"People might choose to go to the PSNI, others will go to lawyers, others will go to representatives of the family."