The IRA's decision to abandon its armed struggle could be the most significant move by a paramilitary group since the Troubles began, it has been claimed.
Dr Brady said he hoped the IRA would follow through on its words
Catholic Archbishop Sean Brady told an audience at St Oliver Plunkett's Church, west Belfast, that he hoped the IRA would follow through on its words.
"I hope that others will respond with the same level of constructive thinking," he added.
He said an "historic threat" from the unionist tradition had to be addressed.
"The statement by the IRA on Thursday was, in my view, potentially the most powerful, significant and welcome move towards genuine freedom in Ireland to have emerged from any paramilitary organisation since the beginning of the Troubles," Dr Brady said.
The head of the Catholic Church in Ireland was giving a lecture on what freedom meant to him as part of Feile an Phobail, the west Belfast festival.
"By setting people free from the fear of violence, by confining the search for freedom to purely democratic and peaceful means, such actions open up the possibility of addressing the deeper and more urgent dimensions of human freedom," he said.
Dr Brady said he hoped that the words of the IRA were followed through and that others would respond with "the same level of constructive thinking".
He said the IRA statement would spark a debate about Irish unity and he hoped that would occur in a "more constructive and less emotive atmosphere".
However, he said it was still unclear to what extent elements of unionism and loyalism were willing to commit to participating in such a debate on purely peaceful and democratic terms.
"Part of the moral complexity of our past was the part played by the threat of violence from the unionist community in the decision to create Northern Ireland as a separate entity," he said.
"What freedom in Ireland means to me is that that historic threat from the unionist tradition is also manifestly and verifiably removed from the debate about our shared future."
The Archbishop also urged republicans to endorse and get involved in policing, arguing society was paying too high a price for their lack of support.
Dr Brady urged Protestant marching organisations and nationalist residents to follow the example of the dialogue about marches in Londonderry which had taken place in an atmosphere of generosity and mutual respect.