The Prime Minister will be tackling the core issue of arms decommissioning as well as the related issues of the shape of the new Northern Ireland administration and new crossborder arrangements.
He will hope to have some solid progress to report when he makes an historic address to both houses of the Irish parliament tomorrow.
Yesterday no one was forecasting a breakthrough on the problem of decommissioning, though movement looks likely on less contentious issues.
Agreement seems imminent on new north-south structures - reportedly in such as areas as waterways and transport - and on the question of how many ministries will make up a new Northern Ireland government. Most parties favour having 10 departments, and although the Ulster Unionists have argued for seven, there is speculation that they may go along with majority opinion.
Other parts of the Good Friday Agreement are moving quietly along, with reviews underway of policing and emergency legislation.
Yesterday the Government announced it was advertising the post of head of a new Human Rights Commission, which is being established under the accord.
The Government described the commission as "a powerful force in developing an active human rights culture in Northern Ireland through education and research".
But time pressure is mounting due to the failure to agree on a new executive. Both Westminster and the Dail in Dublin will shortly need to initiate the legislative processes necessary for a transfer of powers to a new executive by the target date of February.
Mr Blair's key Belfast meetings will be with the Ulster Unionists, who say decommissioning must precede Sinn Fein membership of an executive, and with Sinn Fein, which says entry should depend on no such precondition.
There is no sign of softening of either position. A well-placed source said yesterday: "There's nothing signed and sealed. It's not a case of the Prime Minister coming over and making great announcements. It's a case of working things through with the parties and seeing where we get to after that."
Gerry Adams, Sinn Fein's president, called on the British and Irish governments to "take an urgent joint initiative to stop the drift in the peace process".
A joint assault on racketeering and illegal drug networks will be launched tomorrow when Tony Blair and the Taoiseach, Bertie Ahern, agree to link British and Irish laws targeting proceeds of crime.
The accord, to be signed by the Prime Minister and the Taoiseach during Mr Blair's visit to Dublin, will allow for confiscation of assets held in Ireland by criminals convicted by British courts, and vice versa.
The move is a response to growing links between British and Irish drug networks and money laundering. Detected money laundering through Irish financial institutions rose from IRpounds 30m in 1997 to more than IRpounds 90m this year.Reuse content