The DUP deputy leader, Mr Peter Robinson, yesterday accused the British Prime Minister of propping up a failed political process in Northern Ireland.
The DUP delegation put forward the view of the "overwhelming majority" of the unionist community that continued concessions to the IRA were no longer acceptable, said Mr Robinson.
"He knows the view of the majority of unionists, but we have no confidence that he is prepared yet to take that on board," he said.
His party would table alternative proposals only when Mr Blair had accepted that the Belfast Agreement had failed.
"And that reality he will not be able to deny much longer because sooner or later the people of Northern Ireland at the polls are going to have the opportunity to decide whether it is right for IRA terrorist representatives to be in government while holding on to their weapons," he said.
"Until the moment comes when he is prepared to accept that his present process has failed and is at an end and is prepared to consider an alternative himself, then we will not be putting forward our negotiating position."
PA adds: The Ulster Democratic Party was last night still undecided whether to continue its support for the Belfast Agreement.
After a meeting in north Belfast lasting more than two hours, party officers agreed to meet again next week to discuss the issue. The party chairman, Mr John White, said that a vote would probably take place next week on the way ahead.
He refused to comment on whether any pro-agreement members threatened to resign if the party, which is linked to the Ulster Defence Association (UDA), decided to join the "no" camp.
Earlier this month, Mr Gary McMichael said he would have to reconsider his position as leader if the party opted to change its policy on the agreement.
It is thought that the vast majority of UDA members are now anti-agreement.