Mr Trimble (left) and Mr Durkan: Working together
Stormont First Minister David Trimble and Deputy First Minister Mark Durkan are holding the first in a series of joint meetings with Mr Blair over issues affecting the devolved government.
A spokesman for the multi-party executive confirmed the Ulster Unionist leader and the nationalist SDLP leader were expecting a "range of issues to be discussed" with the prime minister.
"It will be the first joint meeting planned with the prime minister since their recent election to office," he confirmed.
"A range of issues relating to the devolved administration and institutions will be discussed at the meeting, which it is anticipated will be the first in a series of meetings between Mr Trimble, Mr Durkan and the prime minister."
Sinn Fein president Gerry Adams and party colleague Martin McGuinness are also expected to meet Mr Blair on Thursday.
A Sinn Fein spokesman said they would raise allegations of security force collusion with loyalist paramilitaries at the meeting.
The details of Thursday's joint meeting with Mr Blair were confirmed by Mr Durkan in a speech to the Agreed Ireland Forum in Westminster on Wednesday evening.
The new SDLP leader, who took over the mantle from John Hume last month, said he and David Trimble were anxious to discuss "further efforts to continue to build the peace" with Mr Blair.
He added: "Next week David Trimble and I will meet (Irish Foreign Minister) Brian Cowen to iron out a few kinks in the North-South strand (of the Good Friday Agreement).
"And therein, is the challenge, the challenge of good governing, the challenge of the steady, essential work of building the peace."
Mr Durkan also paid tribute to Mr Blair's dedication and commitment to building peace and his understanding of the problems between Britain and Ireland, which he said was greater than his predecessors.
"Together with the parties in Ireland - north and south, unionist and nationalist - he has helped to create an interlocking independent fabric of understanding of the key issues that is unparalleled in the history of our two countries," he said.
Increased stability
The meeting is being held against a backdrop of increasing stability in the devolved assembly, since Mr Blair was last closely involved in developments before his focus turned towards the war in Afghanistan.
Mr Trimble had resigned as Northern Ireland's first minister in July to put pressure on republicans on the disarmament issue.
He placed a ban on Sinn Fein ministers attending the North-South Ministeral Council and then pulled his ministers out of the executive.
But after the IRA's October move on decommissioning, Mr Trimble agreed to stand for re-election with Mr Durkan - then finance minister - as deputy first minister.
The two men were narrowly elected against opposition from anti-Agreement unionists and Mr Trimble lifted the Ulster Unionist sanctions on Sinn Fein.
Last week the executive published its latest programme for government, in which investment in the health service, education and regional development were key planks.
Increasing common ground between the parties on the transition from the Royal Ulster Constabulary to the new Police Service of Northern Ireland, started in November, has also added to a sense of stability.
On Wednesday the Policing Board, which includes members of the UUP, DUP and SDLP, agreed unanimously on a new badge for the service - an issue which had previously caused political controversy.