A Sinn Féin MP, Mr Martin McGuinness, has warned the British Prime Minister that excluding his party from the North's power-sharing Executive would be Mr Blair's "biggest mistake yet".
Mr McGuinness was responding to Ulster Unionist demands at recent negotiations between the two governments and the pro-Agreement parties at Hillsborough, Co Down, for British government action on paramilitary violence.
He said holding Sinn Féin to account for any breaches of the IRA ceasefire would be a "ludicrous situation".
"There is a determined attempt being made by the Ulster Unionist Party, who appear to be setting a context for the battle within unionism for the next Assembly elections, to effectively have Sinn Féin excluded from the Executive.
"We could be on the threshold of seeing Tony Blair make what possibly could be the biggest mistake that he has made in the course of this peace process," the Education Minister told BBC Radio Ulster's Inside Politics.
The British government has been under pressure from hard-line unionists to address their lack of confidence in the peace process before the Westminster parliament rises for its summer recess on July 24th.
It is thought Mr Blair will make a speech before then which might contain a new definition of paramilitary ceasefires.
He is, however, expected to stop short of imposing sanctions on Sinn Féin, re-stating the British government's commitment to the Mitchell principles of non-violence instead.
Speaking on the same programme, however, a UUP MP, Mr Jeffrey Donaldson, said if Mr Blair failed to act decisively on breaches of the ceasefire, such as the break-in at Special Branch headquarters in Castlereagh and republican involvement with Colombian guerrillas his party would be forced to take action.
One possible action could be the resignation of the UUP leader, Mr David Trimble, as First Minister, he added. "People are fed up with the way the IRA are playing fast and loose with the peace process and they expect their leaders to deal with that problem.
"If we fail to deal with that problem there will be electoral consequences," Mr Donaldson said in reference to next year's Assembly elections. One of Mr Trimble's pro-Agreement allies in the UUP, the Arts Minister, Mr Michael McGimpsey, meanwhile questioned Sinn Féin's commitment to the peace process in the light of republican protests against Orange marches.
While this year's Twelfth parades passed off more peacefully than in recent years, Mr McGimpsey said this was evidence that much of the civil unrest connected with them had been orchestrated.
"To attempt to tell people they have no right to express their culture is another way of saying they have no right to exist.
"It questions the commitment to the peace process by some and demonstrates at the very least a lack of tolerance," he added.
Rejecting the UUP Minister's criticism, Sinn Féin MLA Mr Gerry Kelly described Mr McGimpsey as "the Minister from Mars" if he insisted that Orange marches were anything but sectarian.
The PSNI Assistant Chief Constable for Belfast, Mr Alan McQuillan, meanwhile, praised senior republicans for preventing an escalation of violence during a riot at west Belfast's Springfield Road on Friday when an Orange parade passed the predominantly nationalist area. In all, around 100 petrol bombs were thrown, 26 plastic bullets fired and 20 police officers injured in the disturbances. Mr Kelly said nationalists were angry that Mr McQuillan had "demonised" their community prior to the protest by warning of potentially serious riots in the Ardoyne area.
British army engineers have started dismantling the security barrier beside Drumcree church at Portadown, Co Armagh. Apart from a loyalist riot following the annual church service last Sunday, in which 24 police officers were hurt, there were no further protests on Drumcree hill.