The Ulster Unionist leader has expressed confidence that the decommissioning issue will be resolved and that the paramilitaries will be pressurised to move on the matter.
Speaking at a press conference in Belfast yesterday, Mr David Trimble said: "Whether there is movement and whether the movement is resolved satisfactorily depends on the paramilitaries themselves, and, of course, that means all the paramilitaries. "I personally do believe that they will. I believe that the pressure that is there - from the governments and all parties and, indeed, from society on the paramilitaries and their parties to resolve this matter - will be irresistible."
On cross-Border bodies and a power-sharing executive in the North, he said: "There are a couple of issues still to be resolved. I am confident that they will be resolved over the course of the next couple of weeks."
Mr Trimble had no criticism to make of the handling of the decommissioning issue by the British Prime Minister and said he was certain Mr Blair was making his position clear to Sinn Fein.
The UUP leader welcomed Mr Blair's address to TDs and senators yesterday. "It is a significant mark of progress that after so many years a British prime minister has been invited to Dublin and afforded this courtesy."
The DUP leader, the Rev Ian Paisley, said it was disgraceful that Mr Blair had chosen to address the Dail and Seanad before he had addressed the North's Assembly. Dr Paisley said the British Prime Minister's visit to Dublin was a "PR exercise" and he accused him of dodging the decommissioning issue.
The North's Deputy First Minister, Mr Seamus Mallon, described yesterday as "a remarkable day for Britain and Ireland". He said: "Tony Blair's address to the Dail and Seanad confirmed to the world that the days of the old quarrel have passed into history. Britain and Ireland are on a new course, not as aggressors, but as partners."
The Sinn Fein president, Mr Gerry Adams, said he welcomed Mr Blair's visit on one level as it marked the "potential of the new dispensation" in the Belfast Agreement. But he added: "At another level, I hope it isn't premature because, after all, the British are still claiming jurisdiction in the North."