The Democratic Unionist Party's deputy leader, Mr Peter Robinson, said he was no longer reassured on the issue of decommissioning after a meeting yesterday with the British Prime Minister.
Mr Blair was in Belfast for meetings with representatives of all 10 political parties which had taken part in the talks, including the DUP and the UK Unionists, who left when Sinn Fein entered.
Mr Robinson said the best he could get from Mr Blair was that he stood by pledges he had given to the people of the North before the referendum. These concerned decommissioning, policing and prisoners.
The problem, Mr Robinson said, was that there was "a vagueness about the terminology used" in the past. "I told him today that his scriptwriters had left him very considerable flexibility".
Legislation putting the Belfast Agreement into effect would have to make decommissioning a requirement clear, precise terms. Mr Robinson said he had told Mr Blair many people voted for the agreement because they believed Mr Blair's pledges.
"We indicated to him that we would be seeking to hold him to those pledges in every detail."
Mr Robinson said he understood the pledges to mean that any North-South body would be accountable in every respect to the Assembly, that no one in parties linked to paramilitary groups could be a member of a future Northern Ireland government unless decommissioning had taken place, and that prisoners would not be released unless their organisations had ended all violence.
The leader of the Ulster Unionist Party, Mr David Trimble, and the Sinn Fein president, Mr Gerry Adams, emerged from their meetings with Mr Blair with different interpretations of what the agreement meant in relation to decommissioning.
Mr Trimble said he believed Mr Blair would stand by the pledges given before the referendum and that they would be incorporated in legislation coming before the House of Commons.
"His credibility, and not a little of our own, depends on him sticking clearly to the undertakings he gave, and I am quite sure that is his intention . . . The promise is, in simple terms, that if there is not a clear commitment to peaceful means then people will not benefit from this agreement. That applies both to prisoner releases and decommissioning. We are quite sure it will be carried into legislation," Mr Trimble said.
Mr Adams said Mr Blair had made it clear to him there would be no preconditions on anyone, and there would be no rewriting of the agreement.
"He made clear, as any reading of the Good Friday agreement makes clear, that there aren't any preconditions and there can't be any preconditions," Mr Adams said.
The Sinn Fein president added: "If we receive a mandate, we expect to take our positions both in the Assembly and in the executive and in the all-Ireland cross-Border bodies."
Mr Blair repeated yesterday that the RUC would not be disbanded, and there was no question of paramilitaries running the police service. He added: "If we can change the context in Northern Ireland in which policing takes place to one of peace and stability and progress, then hopefully we can get policing done in a normal way which is what all the members of the RUC want, quite apart from the public."