MR Gerry Adams said he has to live in hope that the IRA is open to persuasion to call a new cessation to violence, but he needs a persuasive argument.
The Sinn Fein president said yesterday that the first step on the road back to peace would be to talk to the Taoiseach, Mr Bruton. "What we tried to put together in the past, we must try to put together again," he said in a RTE radio interview when asked if he would attempt to persuade the IRA to call a cessation.
But he said Mr Bruton appeared to have closed that door and he was asking him to reconsider his position. He rejected any suggestion from any source that the organisation he represented was not wedded to a peace strategy. It was the main function of Sinn Fein.
The Taoiseach's refusal to meet left him little room to manoeuvre.
"If he is saying to me that he will not meet me or any of the representatives of those who have voted for us unless the IRA ends its campaign, what room does that give to anyone, when the lesson is that marginalisation under Stormont and marginalisation in the 20 years since Stormont fell achieved nothing?"
Mr Adams said the last breakthrough came when he and Mr John Home began talks and Mr Albert Reynolds took risks.
When it was pointed out that day was now gone, Mr Adams replied: "Well, let's put it together again. Are we going to give up the ghost?
"We are trying to find an agreed solution to a conflict that has affected the lives of people on these two islands for hundreds of years."
He said the responsibility for what had happened in London lay with the IRA, but asked: "Are those who vote for Sinn Fein to be punished for what an organisation over which they have no authority does?"
The IRA had been courageous when it called a ceasefire, but it had done so on the understanding that other things would flow from that decision.
In another of a series of media interviews over the weekend, Mr Adams said Sinn Fein would consider a fresh approach to the IRA but would have to deliberate deeply on when it should do this and what it should say.
Mr Adams emphasised to BBC Radio Ulster that he had no preknowledge of Friday's developments. "My knowledge of this was the same as your knowledge. I picked up all the rumours that were floating about throughout the media and elsewhere late yesterday afternoon (Friday). I then contacted the White House to apprise them of this."
He repeated his criticisms of the British government's lack of movement towards negotiations. "The British have been provocative, they've been negative, there has been no move on constitutional matters, or on the talks to bring those about; there has been no move on democratic matters; there has been no move on the whole necessary issues of discrimination."
He said that, while the unionists had refused to become involved in the political track, Sinn Fein put forward a serious and lengthy submission to the Mitchell commission, and he had welcomed its report. But the British Prime Minister had but the report "in the rubbish bin".
Mr Adams said the London bombing "has to be seen against the background of trying to make peace with enemies and with opponents who weren't prepared to be flexible."
Asked what the last straw had been, he replied: "I don't know. I can only, as I reflect on this, see it as the cumulative effect of a process which many people may have felt was going nowhere."
Asked whether the IRA would have been able to fully accept the Mitchell report, Mr Adams said: "Well, that's a matter for the IRA. What I know is this . . . I said the Mitchell report provided a basis for moving forward into all party negotiation. That remains my position."
Mr Adams also said he was prepared to meet the leaders of loyalism at any time.