Explaining to Ms Ann McCabe why her husband's killers should be released would be "one of the happiest journeys I would make in my life," the Minister for Justice said yesterday.
Mr McDowell said that he believed an historic breakthrough was "possible" in Northern Ireland over the next 48 hours.
He indicated that the killers of Garda Jerry McCabe would be freed only after "a total end to paramilitarism, a total end to criminality, and a total decommissioning of weapons".
Opening a new Community Childcare Centre in Kinnegad, Co Westmeath, Mr McDowell said that if the Government could "bring closure to 30 years of violence and civil disorder in Northern Ireland, and finally write a red line under that whole chapter, going to see Mrs McCabe, if those circumstances arise, would be one of the happiest journeys I would make in my life."
He added: "But I am not going to speculate as to whether that journey will be made because the preconditions for it, which are a complete and proven end to paramilitarism, complete and total decommissioning of all IRA weapons, and an end to all IRA criminality - those things have not yet been delivered and, therefore, I am not willing to speculate as to whether I will be making that journey."
Mr McDowell did not wish to be drawn on the suggestion from the Garda Representative Association (GRA) that they would seek legal advice to oppose the release of the four killers, who are currently serving sentences in Castlerea Prison.
"It's up to the GRA to take legal advice as they see fit. But I have consulted with the Garda Representative Association in this matter," he said.
"I have kept them fully informed of where things are at at the moment, and I will keep them fully informed if there are any developments."