The Ulster Unionist Party has welcomed Senator George Mitchell's statement which, it says, recognises that devolution for Northern Ireland and decommissioning should begin as quickly as possible.
The senior UUP negotiator, Sir Reg Empey, said: "We also agree that the Independent International Commission on Decommissioning should play a more central and proactive role in securing disarmament.
"Ulster Unionism recognises the challenges and difficulties faced by the leadership of Sinn Fein/IRA. Nevertheless, we call on them to respond positively to this process and to state clearly their commitment to achieving decommissioning.
"If unionism is to deliver an inclusive executive, republicanism must deliver decommissioning. Both sides must demonstrate in word and deed their commitment to these issues respectively if the agreement is to work."
He said his party was committed to seeing an executive set up, founded on the Belfast Agreement's principles of democracy and moral integrity. "We will continue to do our best to make the review a success," he added.
Mr Gerry Adams said Senator Mitchell's positive assessment of the review was "clear evidence of progress". The Sinn Fein president stated: "We share his increasing confidence that the review process has the potential to achieve a resolution of the current impasse in the peace process.
"We welcome his assessment that the institutions should be established at the earliest possible date. The central role of Gen de Chastelain's commission is also underlined.
"This review was established to resolve the crisis in the peace process by ensuring the full implementation of the Good Friday agreement in all its aspects. This is the only context for addressing all of the outstanding issues."
Gen de Chastelain, who is chairing the decommissioning body, said he had given his assessment on the weapons issue to Senator Mitchell and the political parties and it would be made public very shortly. "We have a job to do and we look forward to getting on with it," he said.
Mr John Hume described Senator Mitchell's report as "encouraging". The SDLP leader said: "His increasing confidence that we can find a way forward to resolve this impasse is significant."
The SDLP also welcomed Gen de Chastelain's statement and urged paramilitary groups to "engage directly and co-operatively with the commission" and to "respond positively to (its) call for the appointment of authorised representatives".
The DUP deputy leader, Mr Peter Robinson, said the statements by Senator Mitchell and Gen de Chastelain showed how "feeble UUP resistance to Sinn Fein's demands have been".
Mr Robinson said: "The de Chastelain assessment effectively says there will be no guns before Sinn Fein is in government and even then it will be a voluntary act. The appointment of an IRA interlocutor does not amount to anything remotely close to the requirement for actual product to be surrendered.
"No amount of spin or hype can make a demonstrably immoral and corrupt capitulation into a good deal for unionism."
The Northern Ireland Unionist Party Assembly member, Mr Norman Boyd, said the likely deal was totally unacceptable.
The Alliance Party leader, Mr Sean Neeson, welcomed the two statements. "Hopefully, we can now move positively forward and implement in full the people's agreement reached on Good Friday last year."
The Northern Secretary urged the politicians to move the peace process forward for the public good. Mr Mandelson said: "We either go step by step into the future or let fear of failure destroy our chance of success.
"The people want us to give it a go. They want to live in a decent, democratic society, a society with devolved government, and in which arms have been decommissioned. Both goals can and must be achieved.
The SDLP deputy leader, Mr Seamus Mallon, warned last night that "We have not finished this review yet, we have some distance to go - the final furlong in racing terms - and that is going to be the difficult part of this journey."
On Channel 4 News he appealed to unionists and republicans not to fail.
"We have heard, and will hear in the next few weeks, how difficult this is going to be for unionists and how difficult it is going to be for republicans. But I tell both of them - it is going to be very difficult for everybody if this review doesn't work."
The UUP security spokesman, Mr Ken Maginnis, and the Sinn Fein senior negotiator, Mr Gerry Kelly, interviewed together on the same programme, appeared to go out of their way to support each other.
Mr Maginnis said he realised "republicans do have a problem, a huge problem with disarmament". Mr Kelly said he understood "unionist have big problems to bring this to their constituency".
Meanwhile, a UUP assembly hardliner, Mr Peter Weir, predicted that if Mr Trimble took the deal to the party's ruling Ulster Unionist Council and got backing "a split in the party would be inevitable".