Mr Trimble, the Ulster Unionist leader, came close to being forced to resign amid last week's crisis in which the peace process was almost shattered. He is now likely to stay, although no formal announcement will be made before he returns from a three-week holiday, which started yesterday and effectively confirms that the peace process has been "parked".
Meanwhile, the former US senator George Mitchell, who chaired the multi- party talks that led to the Good Friday Agreement, is to meet Mr Blair and the Irish Prime Minister, Bertie Ahern, in London tomorrow. He is likely to be given a substantial role in the review process.
The Prime Minister has urged Mr Trimble to stay on as the head of the stalled Northern Ireland power-sharing executive in spite of the impasse over the IRA's failure to begin decommissioning its weapons.
Mr Trimble said: "If I were to resign would that not make it appear that the position is crumbling further, that the process is disintegrating further? I have to think about that - and I am thinking about that."
He said that both the British and Irish governments were briefing journalists that they thought he should remain in office. He said that despite the resignation of the Deputy First Minister, Seamus Mallon, the SDLP deputy leader, it would send a signal that the political process was disintegrating if he followed suit.
He had to consider what was best for the political process - "what is more likely to sustain confidence in it and what is likely to undermine that confidence". While saying he got on well with Mr Mitchell and had great regard for his abilities, Mr Trimble said that in the end the problems had to be sorted out by the local parties. The business of "always running to somebody else", whether it was Mr Blair or Mr Ahern or Mr Mitchell, was not a healthy way to proceed, he said. It was used by parties as an excuse for not engaging with each other.
Amid growing speculation that the Northern Ireland Secretary, Mo Mowlam, is about to leave the Northern Ireland Office in the cabinet reshuffle, Mr Trimble refused to say who he wanted to take the post. Frontrunners are thought to be Peter Mandelson - who would be making a return to Cabinet after six months on the back benches - and Paul Murphy, the political development minister who has been Ms Mowlam's number two in Belfast.
Mr Trimble said he would work with whoever was appointed, and questioned whether the Prime Minister should continue to have such a hands-on attitude to the Northern Ireland situation. "Whether it is the best way to proceed, I am not sure," he said. "I felt really embarrassed at the end of June... to see the Prime Minister of the United Kingdom sitting in Castle Buildings for five days doing the work that really should be done by a junior minister.
"That's not good for the Government of our country and I am concerned he will come under increasing criticism in London and throughout the kingdom for spending too much of his time on the Northern Ireland situation."
On BBC Radio Ulster's Inside Politics, Mr Trimble said Mr Blair's closeness to the issue also had a bad effect on the Northern Ireland parties. "We were in a situation that nobody would do any serious talking until the Prime Minister arrived. I think we have to get away from that, from this nursemaid attitude, to doing the job for ourselves," he said.Reuse content