The head of the Catholic Church in Ireland has called for the disbandment of the IRA.
Dr Brady said there was no need for violence in a democratic society
The Archbishop of Armagh, Dr Sean Brady, was speaking for the first time since a wide-ranging speech in London on Wednesday.
Dr Brady told the BBC's Sunday Sequence programme that there was no need for violence in a democratic society.
"We must dispel any ambivalence in our own community about the presence or actions of non-democratic and totally unaccountable armed groups in our own community," he said.
"I am calling on people to forsake once and for all the armed struggle."
Dr Brady received a mixed reaction for last week's speech, in which he criticised the government for failing to tackle the issue of collusion.
He described as "unacceptable" the delay over a public inquiry into the murder of the Belfast solicitor Pat Finucane.
Dr Brady said he wanted to highlight what he saw as the main issues on the way to finding a resolution.
He added that the political parties must go the "extra mile" to bring about police reform.
DUP assembly member and Policing Board member Ian Paisley Junior welcomed Dr Brady's comments, having earlier criticised last week's speech as unhelpful.
Mr Paisley said on Sunday that Dr Brady had "gone some way to clear up the confusion surrounding what he had originally intended to say".
The Chief Constable, Hugh Orde, described Dr Brady's speech as balanced.
However, in a statement on Thursday, Mr Orde said that some parts of the speech that had been highlighted did not give a true reflection of its overall balance.
The vice-chairman of the Policing Board, Denis Bradley, described Dr Brady's speech as "helpful".
Mr Bradley said the archbishop helped highlight some of the problems communities had over policing.
Dr Brady said that Protestants had to accept the full implications of the Good Friday Agreement and the legitimacy of the nationalist aspiration to a united Ireland.
And he called for Catholics to "vigorously challenge" the actions of "non-democratic armed groups".
He described Northern Ireland as a society with an "inherent capacity to distrust".