Ulster Unionists last night called for the Sinn Féin President, Mr Gerry Adams, to provide further clarity on the issue of paramilitary activity.
Mr Michael McGimpsey, a former minister in the Executive, said it was essential that all remaining doubt be cleared away and that the next Assembly election mark a clear departure from the past.
He said it was necessary for politics to proceed in Northern Ireland in a climate where there was no doubt about the linkage of any party to what he called "private armies".
However, speaking against a backdrop of continuing campaigning among rival unionist parties, the DUP dismissed the Adams statement as a stunt.
Mr Nigel Dodds said Mr Adams had merely used "yet more hollow words. It is a cynical election stunt which will fool no sensible unionist in Northern Ireland," he claimed.
The former minister added: "A qualified clarification of Tony Blair's three meaningless questions does not move us one iota closer to the day when Sinn Féin enters the democratic process.
"Gerry Adams's statement is yet more hollow words which have had to be dragged out of the man who told us he was never in the IRA."
The SDLP welcomed the statement as "another step forward" which Mr David Trimble should not discount.
Mr Alex Attwood, the party chairman, said: "Given that we have had a drip of statements and clarification over recent days and weeks, people generally find it difficult to judge for themselves the progress that has been made and the gaps that may remain."
He said all the statements, the issues of clarification and the two governments' joint statement should be published so that the public could make up their own minds.
Asked if he thought the IRA was saying it was ending paramilitary activities, Mr Attwood said: "If, three weeks ago, all the clarification had come out at that time, then people would have had the confidence, the clarity and certainty they were seeking."
He said the publication of everything was needed. "If we can see all, then we can judge all," he said.
Echoing the qualified welcome of the statement by the two governments, Mr Attwood said the UUP leader should not dismiss Mr Adams's comments out of hand.
Sinn Féin's chief negotiator, Mr Martin McGuinness, showed clear exasperation at the reaction to the statement. He claimed republicans had bent over backwards to try to facilitate political progress.
"At the core of this is the fact that David Trimble has been in anti-agreement mode since last year. He refuses to defend the Good Friday agreement, he refuses to promote it, he refuses to embrace it and he has effectively decided to be in anti-agreement mode alongside the Rev Ian Paisley."
He said the IRA had provided the British and Irish governments with a statement which he insisted was "clear and unambiguous".
He also repeated that Mr Adams had spoken about that statement in terms which had been widely welcomed. On that basis, he added, he was not "going to get into a word game".
"I am sure that people will recognise the huge contribution that Gerry Adams has made in the course of recent days to explain the republican position. If the unionists are not prepared to accept that, I think it ill behoves the rest of us."
Mr Bill Flynn, chairman of the National Committee on American Foreign Policy, urged the two governments and Mr Trimble to accept Mr Adams's statement.
He said: "We at the National Committee are totally satisfied that the republican movement is committed to a complete cessation of all those activities inconsistent with the Good Friday agreement, all of those activities that are inconsistent with a peaceful democratic society and all of those activities inconsistent with the rule of law."