The SDLP has welcomed Mr Gerry Adams's statement and expressed the hope that there will be an immediate move on Provisional IRA disarmament.
Mr Mark Durkan, who will succeed Mr John Hume as party leader next month, said he hoped there would soon be a statement from the Independent International Commission on Decommissioning.
"We hope, like other parties, to be in a position to receive a positive and authoritative report from Gen de Chastelain on this whole issue", Mr Durkan said. "The sooner it comes the better. I would hope, now that Sinn FΘin have put on record that they have counselled the IRA, the IRA will be able to demonstrate what conclusions it has come to."
Mr Hume said: "I welcome Gerry Adams's request to the IRA to resolve the arms issue and hope they respond positively. "I hope David Trimble will also respoitively by ensuring that all the institutions remain in place and by ensuring they work together to build a new society."
The leader of the Alliance Party, Mr David Ford, welcomed Mr Adams's statement but added: "Real action is now needed within a short time. The hope engendered by this statement will be useless unless it is followed by IRA action to remove weapons from use to the satisfaction of the Independent International Commission on Decommissioning."
Prof Monica McWilliams, an Assembly member for the Women's Coalition, said: "It has always been our view that the referendum was the call of the people and expressed their desire for decommissioning. We are pleased to see that Gerry Adams's statement addresses the IRA and calls on them to stay in touch with that call. The people have asked for a confidence-building measure and Adams acknowledges that the IRA have the power to transform the current stalemate. Progress for Northern Ireland demands ground-breaking actions but also a ground-breaking response."
The president of Republican Sinn FΘin, Mr Ruairi ╙ Bradaigh, described Mr Adams's statement as a "complete betrayal of republicanism".
He added: "It is the worst yet. Other people, like Collins and de Valera, betrayed republican principles but never went this far. The price to be paid for it all is to repress the republicans who would continue with the struggle."
Mr Rory Dougan, of the 32-County Sovereignty Movement, said he was not surprised by Mr Adams's statement. "We have been predicting these such events since 1997. The Sinn FΘin statement focused on policing, demilitarisation and equality for nationalists within the six-county state. The absence of demands for Irish freedom and the ending of British rule was noticeable. These have always been the cornerstone of Irish republicanism."