The incoming leader of the SDLP, Mr Mark Durcan, who takes over next month from Mr John Hume, welcomed the IRA move which he said "should be well received within the community and the political process as a significant contribution in the implementation of the agreement".
Mr Durkan added: "Parties should use these positive developments to renew their commitment to make all other aspects of the agreement work, including bringing all the political institutions into their fullest and most inclusive operation."
He also praised the work of the Independent International Commission on Decommissioning.
Sinn FΘin's national chairman, Mr Mitchel McLaughlin, said the move was a very significant development, but needed a positive response.
"This move by the IRA rekindles all the hope and expectation that was created at the time of the Good Friday Agreement," he said. "Obviously it requires other political leaders to further develop the peace process by making the political system work and enabling those functioning within it to carry out their functions and responsibilities.
"It is incumbent on the political leaderships to respond to this opportunity and on the two governments to move speedily to remove the remaining difficulties on issues like policing, demilitarisation, the reform of the criminal justice system, equality and human rights," he said.
The leader of the Northern Ireland Women's Coalition, Prof Monica McWilliams, said yesterday's developments were proof that the political process could work. "All along we have been saying that these things take time. Up to now we have been managing the process - from now on we can hopefully start to transform it."
The outgoing SDLP leader, Mr John Hume, has said unionists must respond positively to the Provisional IRA's action on decommissioning. He welcomed all movement on the weapons issue.