The Ulster Unionist Party MP, Mr Ken Maginnis, has said that while he wants to see actual Provisional IRA decommissioning, the paramilitary group's statement could provide the basis for moving forward.
"I'm unhappy that we haven't more from the IRA," he said. "I want to see the guns and explosives. But sometimes it is small steps that eventually help us reach our goals. If you put the IRA statement with the Sinn Fein statement, we have made some progress.
"While this isn't enough, it is the only option open to us at this time to achieve what we ultimately want. We then have to establish trust between the two traditions, and that will be a question of disarmament."
A UUP negotiator, Mr Michael McGimpsey, said the Provisional IRA statement could be a step towards achieving his party's two aims of decommissioning and devolution.
He said the way could be open to setting up an executive: "There is a possibility we may be in business here." The importance of the statement was that, unlike previous ones, it did not rule out decommissioning.
However, the anti-agreement UUP MP, Mr Jeffrey Donaldson, dismissed the statement as "totally inadequate".
"There is no timetable, no declaration the so-called war is over, absolutely no guarantee that decommissioning will every happen. I will be urging our party not to accept it or we will be in breach of party policy," he said.
The dissident UUP MP, Mr Willie Thompson, urged Mr Trimble to resign and said he would leave the party if it accepted the deal.
Another dissident, Mr Willie Ross MP, said the statement was of no benefit to unionists and there was no chance of any decommissioning.
The UUP deputy leader, Mr John Taylor, was not available for comment. He is in Iran on parliamentary business and does not return until tomorrow.
The DUP deputy leader, Mr Peter Robinson, said the statement offered no guarantee on decommissioning.
"We were told that it had to be guns before government. This statement not only doesn't deliver guns before government, it doesn't even have the promise of guns at some later stage," he said.
A DUP Assembly member, Mr Sammy Wilson, claimed that decommissioning was even less likely, because "the IRA now know that David Trimble and his negotiators have no backbone and can be treated as putty in their hands".
The Northern Ireland Unionist Party leader, Mr Cedric Wilson, said the statement was even worse than he had anticipated.
"We expected the wordsmiths in Sinn Fein/IRA to come up with better than this. It is now up to ordinary UUP members to stop Mr Trimble - and his plans to put terrorists into government - in his tracks. Nobody else can do it but them," he said.
The Ulster Democratic Party leader, Mr Gary McMichael, said the statement was "the most positive and precise" from the Provisionals since their ceasefire.
Unionists would recognise it as "a valuable step forward".