The Prime Minister held talks with Mr Trimble and Sinn Fein's chief negotiator, Martin McGuinness, in an attempt to find a way through the impasse, but there was no sign of compromise on either side.
The Ulster Unionist leader and First Minister is refusing to set up a new power-sharing executive with Gerry Adams, Sinn Fein's president, and Mr McGuinness as ministers in Northern Ireland to appoint the bodies until the IRA has started to hand over its weapons.
The Prime Minister's office insisted the 31 October deadline for establishing the executive and cross-border bodies must be met. "It is not a target. It is a deadline," said Tony Blair's official spokesman.
Mr Trimble is facing a critical meeting of the Ulster Unionist annual conference on Saturday, and ministers privately said that was complicating the search for a solution.
The Dublin and London governments are planning to spend the next few days in intensive talks to find a face- saving formula, including the decommissioning body, headed by the Canadian general John de Chastelain. It is understood that ministers are hoping to publish a clear timetable for decommissioning over the next two years to meet the terms of the Belfast agreement and give Mr Trimble guarantees that progress on arms surrender is not being quietly dropped.
Mr Blair hoped that the euphoria over last week's award of the Nobel Peace Prize to Mr Trimble and John Hume, leader of the Social Democratic and Labour Party, for their commitment to peace in Ulster, would smooth the way through the crisis over the deadline, but there was still deadlock last night.
Mr McGuinness speaking in Downing Street, after meeting Mr Blair for more than an hour, said that Mr Trimble should use the strength of his joint award with Mr Hume, to "face down" the hardliners in his own party.
"I think David Trimble has considerable room for manoeuvre. The award of the Nobel Peace Prize has put him in an unprecedented strong position and I think he should use that new strength to face down the leadership of the Ulster Unionists' parliamentary party who are absolutely dedicated to the destruction of the peace process," Mr McGuinness said. Mr Blair and Bertie Ahern, the Irish Prime Minister, and their officials are in daily contact to find a breakthrough, and they are expected to discuss the crisis in the margins of the European summit in Austria on Saturday.
A Whitehall source said: "The IRA official position is that there is not going to be decommissioning. Sinn Fein are saying they will implement the agreement, and Trimble is saying we are not having the shadow executive without it.
"There is scope within all of that for flexibility on all sides, but it will have to be movement on all sides. It won't work if only one side is forced to back down."
The Tory MP Andrew Hunter said: "I don't think there will be a way out of this unless Mr Trimble gives way. I think he wants to give way. The problem is that his own position would then be at risk. I don't think there are grounds for optimism."
Mo Mowlam, the Secretary of State for Northern Ireland, was in Chicago on the second leg of an 11-city tour to raise investment in the province as part of the peace bonus to be earned after the agreement. Ministers were not prepared to contemplate the possibility of the agreement breaking down, but they privately admitted that the position was serious.Reuse content