But despite the lack of agreement, Mo Mowlam, the Secretary of State for Northern Ireland, refused to characterise their ending as a breakdown, saying they were part of a process and that bilateral talks would continue next week.
The talks were regarded as a last-ditch attempt to avert a repetition of last year's tumultuous marching season, when disturbances which began at Drumcree, near Portadown, Co Armagh, spread to many areas of Northern Ireland.
The Orange Order said after the talks, which lasted for more than seven hours, that it had put forward what it believed were responsible and accommodating principles which respected the rights of everyone.
It appealed for calm at what it described as a sensitive time, asking its members to act responsibly.
Catholic residents from the Garvaghy Road said that they had had useful and constructive exchanges with Dr Mowlam but added: "Unfortunately, the Orange Order were not willing to pursue a similar path with us directly. We want to sit down with the Portadown Orangemen to find a lasting and just solution."
While the residents' spokesman, Brendan McKenna, said the talks had ended, Dr Mowlam would not accept they had broken down.
She said: "It is very clear that it is not a breakdown. I called the talks to an end for the simple reason that I thought we had gone over the issues during the day and had a number of suggestions from both sides. I want a chance to think about those and go back and talk in bilaterals next week."
The government-sponsored talks opened yesterday morning on the neutral ground of Hillsborough Castle, Co Down.
The fact that the two sides had agreed even to this limited form of discourse was regarded as an advance in itself, but the surrounding atmospherics have been anything but promising. The Orange Order insists on the right to walk down Garvaghy Road after its Drumcree church service; Catholic residents insist they have the right to say no.
Meanwhile, the IRA's campaign of violence persists, with police escaping injury in a rocket attack on vehicles in north Belfast late on Thursday night.
The message from republicans appears to be that, while the idea of a renewed ceasefire is not ruled out, the IRA feels free to carry out such attacks up to the point any new cessation comes into effect.
In the Irish Republic, police were investigating a suspected IRA terrorist training camp close to the border in County Cavan. It was not known whether the camp had been in recent use.Reuse content