There will have to be a "genuine process of national reconciliation" between unionists and nationalists and the Government would have a key role, Sinn Féin president Gerry Adams told the party's annual 1916 commemoration at the GPO.
Its first step would be to "start thinking, acting and legislating with an eye to the needs and rights of every citizen on this island."
Mr Adams said there had been "a move away from armed struggle to political negotiations and now political agreement between Sinn Féin and the DUP and the recent amicable meeting between Ian Paisley and the Taoiseach."
Sinn Féin was ready for government, North and South.
About 1,000 people marched from Parnell Square to the GPO where a statement from the IRA army council was read out, in which it said that a united Ireland could be achieved through "purely peaceful and democratic means".
Asked afterwards why the IRA had not "gone away" Mr Adams said "you have to appreciate the content of the statement and the commitment to peaceful and democratic means" to achieve a united Ireland. He added that "we are in a transitional process".
He saw no symbolism in the fact that Dr Paisley shook hands in public with the Taoiseach and had not yet shaken hands with him.
:quality(70)/s3.amazonaws.com/arc-authors/irishtimes/5cf4f137-e78e-4bdb-a43b-6311e855e51f.png)