The British Prime Minister's chief of staff, Mr Jonathan Powell, has put forward two sets of proposals to Portadown Orangemen and the Garvaghy Road Residents' Coalition in an attempt to resolve the Drumcree parade dispute.
The proposals, which include face-to-face talks, to be chaired by a British government minister, between the legal and political representatives of both sides, were tabled during separate meetings with representatives from both sides at Stormont House yesterday.
In a statement issued after the meetings, the Northern Ireland Office said the Orange Order and Garvaghy Road residents "agreed to consider the proposals" tabled by Mr Powell.
Both sides are also considering the proposal to establish a Portadown forum and the putting together of an economic package for the Co Armagh town.
The political and legal representatives representing both sides involved in the dispute will also meet the Parades Commission to discuss a range of issues.
The meetings were "useful and workmanlike," said a government official.
However, Mr David Jones, spokesman for the Orange Order, said that while the proposals would be discussed with members of the Portadown Orange Lodge, face-to-face talks between Orangemen and residents were ruled out.
"The district officers will not be having any contact with the Garvaghy Road Residents' Coalition. We have made that quite plain from the start," said Mr Jones.
He added the meetings would be time-limited and could be finished by the end of this month. "We are still on the hill at Drumcree, we remain at the hill until the matter is resolved and we believe the matter will be resolved in August . . . We see this as being the end of the process," he said.
The Portadown Orange Order spokesman added that while they were prepared to look at the government's proposal they also believed that there should be a deadline on the process.
However, Mr Breandan Mac Cionnaith, spokesman for the Garvaghy Road Residents' Coalition, ruled out any more talks taking place until residents had met Mr Blair when he returns home from his holiday, which will not be until the end of August.
The Orange delegation, which included Co Armagh grand master Mr Denis Watson and Portadown district master Mr Harold Gracey, said they would enter into further dialogue after today's meeting only if they felt it could resolve the dispute.
Mr Jones acknowledged that Mr Blair had shown "a greater understanding" of the Orange Order's position and an appreciation of its flexibility in recent weeks, but said they could not continue talking ad infinitum.
Earlier, Mr Mac Cionnaith said there was "a realisation on the part of the British government and an acceptance" that proximity talks between the Orange Order and residents had failed.
"I think it is fair to say that there is a realisation on the part of the government and an acceptance of what we have been saying for a long time, that the proximity talks format is a failed format and the governments will examine other ways of how to move us into direct talks with the Orange Order," said Mr Mac Cionnaith.
"We have always said this is a whole question of equality and showing respect and dignity to each other and the Orange Order is going to have to take the step of sitting down face to face with us."
Yesterday's meeting is the fourth attempt by Mr Blair's chief of staff to end the standoff at Drumcree in Portadown. In July 1998, Mr Powell chaired proximity talks in Armagh, using nationalist and loyalist intermediaries, but failed to find a solution. He renewed his efforts last December, but this also failed.
And in June, while Mr Blair and the Taoiseach, Mr Ahern, were taking part in negotiations at Stormont to resolve the decommissioning and devolution impasse, Mr Powell was a central figure in Mr Blair's efforts to break the deadlock over the Drumcree parade.