Dublin reaction: President Mary McAleese has said she hoped the IRA statement would help to secure the long-term, peaceful and respectful co-existence of all people on the island of Ireland.
She said the statement offered "a real opportunity to build the trust and mutual understanding on which a just, equitable and peaceful future will rest".
Praising all who had worked to eradicate the armed struggle in Ireland, Mrs McAleese said: "I hope that in the interests of generations to come, this opportunity will now be well and wisely used.
Tánaiste Mary Harney described the statement as "a knock on the door of democracy" and said it had the clearest potential to date to achieve "an enduring and lasting peace".
People would "now expect to see the IRA act immediately and to demonstrate with maximum transparency their newly stated commitment to pursue Irish unity through exclusively peaceful means".
She commended Taoiseach Bertie Ahern and British prime minister Tony Blair for making "an outstanding contribution to the Northern peace process throughout the past eight years".
She also referred to the 3,000 people who had died in the Troubles. "Their loss can never be compensated but my hope is these families will take some small comfort from today's commitment by the IRA to finally cease their military campaign and embrace democratic politics."
Fine Gael welcomed the statement as having "the potential, if fully delivered on, to repair the damage done to public confidence in the Northern peace process".
The party's deputy leader, Richard Bruton, said the sincerity of the statement "will be judged by the actions it takes".
It also rejected "the notion that the IRA would be allowed to organise commemorations of its past atrocities as this would only serve to inflame sectarian tensions on an ongoing basis".
Fine Gael leader Enda Kenny is to seek a meeting with Mr Ahern to establish if any concessions were granted to Sinn Féin in advance of the IRA statement.
Labour Party leader Pat Rabbitte said the statement was a "hugely significant development" and if fully honoured, had the potential to herald "a new era of peaceful and democratic politics in Northern Ireland".
He cautioned that because of "so many false dawns" since the original ceasefire in 1994, the IRA would have to show "by deeds and not by words" that it had rejected violence and criminality.
Green Party leader Trevor Sargent said the statement was "good news and an important moment".
"If indeed the blockage that the IRA and its activities represented has been removed, in a way that can be proven, then the onus is now on the DUP to return to the power-sharing structure of the Assembly so that the democratic institutions in Northern Ireland can be restored."