The Prime Minister has invited Mr Adams and the key party leaders in the Northern Ireland peace process to his conference hotel for a series of "hot house" meetings to try to find a solution to the stand-off.
It is a mark of how far the Northern Ireland peace process has travelled that Mr Adams was invited as a guest of the party to hear Mr Blair's speech, in which he called on the political leaders to "close their ears to prejudices of their own parties and listen to the prayers of the people for peace".
Mo Mowlam, Secretary of State for Northern Ireland, was given a standing ovation after Mr Blair praised her role in the peace settlement.
But the gap between the Sinn Fein leader and David Trimble, the Ulster Unionist leader, over the decommissioning issue was underlined by Mr Adams.
He accused the Unionists of seeking to reopen the Good Friday Agreement. He said the Unionists "cannot renegotiate. They will need to keep their promises".
Mr Adams, who heard Mr Blair's speech in an overspill hall after being delayed on his way to Blackpool, last night used a Tribune rally there to call for Mr Blair to work with him towards a united Ireland.
The Government could not claim to be a neutral "referee" between nationalists and unionists, he said. "To uphold the union means using repression, denying civil and human rights and defending equality and injustice. If there is to be change there needs to be new thinking in Labour."
Mr Trimble, First Minister in the Northern Ireland Assembly, will not let Mr Adams and his deputy Martin McGuinness to join the power-sharing executive, which is stalled, until the IRA starts decommissioning.
Mr Trimble accused Sinn Fein of breaking the spirit of the agreement by so far refusing to make headway on the issue. "If they are voluntarily saying they refuse to carry out their obligations under the agreement then there is not going to be confidence. It is a question of their need to create confidence."
Mr Blair is expected to tell Mr Adams that the Government has made concessions to build confidence in the nationalist community by withdrawing more troops from the streets of Northern Ireland.
He will point out that the Government is keeping its side of the bargain and will say that it is time for the IRA to deliver on Sinn Fein promises.Reuse content