Despite protests from the Conservative Party that a meeting would be "premature", the Prime Minister is expected to visit Northern Ireland this week.
A meeting with Sinn Fein would be the first event of its kind since the start of the violence in Northern Ireland 28 years ago and is likely to provoke criticism from Ulster Unionists.
But following the IRA cease-fire and the admission of Sinn Fein into round table talks, the Prime Minister is committed to treating Mr Adams like any of the other party leaders.
Most of his allies believe that the sooner the symbolic meeting is out of the way, the better. Marjorie Mowlam, Secretary of State for Northern Ireland, has already met Mr Adams.
The format of the meeting remained unclear yesterday. One option is that Mr Blair welcomes the parties at round table talks at Stormont tomorrow. That would have the advantage of keeping the encounter away from the cameras, as talks take place in private. When President Clinton met Mr Adams he ensured they were not photographed.
However, some feel that Mr Blair's presence tomorrow would look contrived since the talks are already under way. The alternative is to combine a meeting with a general visit to Belfast.
The new US ambassador to London, Philip Lader, will visit the province this week and will meet Mr Adams or his colleague, Martin McGuinness. Mr Lader, who is visiting at the invitation of John Hume, leader of the SDLP, will also see other party leaders and Dr Mowlam.
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