The Foreign Minister, David Andrews, congratulated Sinn Fein and the Unionists for "the courage and leadership they are showing". Mr Andrews added: "These generous and visionary statements represent a further important step towards a resolution over the full implementation of the Good Friday Agreement."
The Social Democratic and Labour Party reaffirmed its commitment to implementation of the agreement, saying it was a chance to "transcend our past, to leave behind division and conflict for once and for all.
"While frustrated at the slow progress, we have continued to urge all involved to be generous and flexible, and, for the sake of all our people, to put aside narrow party or sectional interests. We have been preparing policies for the new administration's programme of government ... as well as detailing the tasks to be undertaken by these bodies.
"The SDLP is determined that all the new political institutions will succeed not just in building new relationships but in making a real difference to the lives of all of our people. [The agreement] achieved an emancipation of hope. Our collective task now is the emancipation of opportunity. There is no more time to waste."
The Ulster Democratic Party also welcomed the developments, which it viewed as providing a real opportunity for the full implementation of all aspects of the agreement. But the UDP, which speaks for the loyalist paramilitary Ulster Defence Association and the associated Ulster Freedom Fighters, made no direct reference to decommissioning in its statement.
The party said the review process had been "a pathway whereby the twin goals of a stable executive and a resolution to the conflict are now achievable. It remains for Northern Ireland's political representatives to rise to the challenge."
It singled out the stewardship of the talks by retired US senator George Mitchell, saying: "We pay tribute to the patience, tenacity and political skill of senator George Mitchell without whom we would not have reached this point. Northern Ireland owes Mr Mitchell a deep debt of gratitude."
The Progressive Unionist Party, also linked with loyalist paramilitaries, said decommissioning was integral to the peace process but not a pre-condition for inclusion in government. The party, the political wing of the Ulster Volunteer Force and the Red Hand Commando, also vowed to continue to work with the independent commission to achieve disarmament. "The removal of illegal [arms] is an integral part of the conflict transformation process taking place in Northern Ireland," said the PUP's Billy Hutchinson.
Mr Hutchinson is the only direct representative of paramilitaries, the UVF and RHC, appointed to speak directly to the decommissioning body. Mr Hutchinson said: "The Progressive Unionist Party does not see decommissioning as a pre-condition to access to the structures envisaged in the Good Friday Agreement, whilst we recognise that it is an issue that must be dealt with."
The Alliance Party also urged the establishment of the executive as soon as possible and a start to decommissioning, as facilitated by the "authorised representatives. General de Chastelain and his team must be given full co-operation and commitment by all groups holding illegal arms and explosives," a statement said.