The Orange Order has rejected fresh calls from the Parades Commission to begin negotiations with nationalist residents' groups who oppose loyal order parade routes through their areas.
The chairman of the commission, Mr Alistair Graham, yesterday urged the Grand Lodge of Ireland to talk to residents after the July 12th marches passed off peacefully in Belfast, Portadown and other locations across the North.
"We will not be talking to Sinn Fein/IRA-orchestrated residents' groups, and the sooner that sinks into Mr Graham's and his minions' heads the better," insisted Mr Denis Watson, the County Armagh Grand Master.
"I am certainly not going to sit down and negotiate why I should have my rights restored. They should never have been taken off me in the first place."
However, Mr Graham has stressed that substantive engagement is the only way forward for both sides.
Orangemen in Portadown and Ballynafeigh, south Belfast, were this year prevented from marching through nationalist areas as a result of rulings from the commission.
Speaking on BBC Radio Ulster, Mr Graham said residents' groups needed to demonstrate to Orangemen that it was worthwhile entering into engagement.
"There is no point in having dialogue and engagement if you have the feeling you are not going to reach an accommodation, ever.
"There has to be a mutual willingness to try and make some progress on these issues. If that happens then the role of the Parades Commission becomes something of an irrelevancy and nobody will be happier if that was to develop in the new world."
The Northern Secretary, Dr Mo Mowlam, praised the Orangemen for "working hard" to keep the Twelfth celebrations trouble-free. She said those opposed to the marches had expressed themselves in an equally restrained manner.
"We now need to build on that experience and try to reach local accommodations that would permanently remove the potential for conflict.
"That, I hope, we can do, but it is important that we all acknowledge the very real efforts that have gone into ensuring that the past week has been as peaceful as it has."
Meanwhile, statistics issued by the RUC yesterday highlighted the peaceful nature of the Twelfth marches in comparison with last year.
The number of plastic bullets fired by the security forces dropped from 823 last summer to just one this year.
Both figures relate to periods from the Drumcree march to yesterday.
Petrol-bombing incidents decreased from 625 last year to 17 this year.
In total, there were 614 public order incidents in 1998 but just 43 this year.
Arrests also dropped from 266 last year to 49 for 1999.
The RUC Chief Constable, Sir Ronnie Flanagan, said: "So far, this shows what can happen when people exercise that degree of tolerance."
According to the Assistant Chief Constable for Belfast, Mr Bill Stewart, Monday passed off not just peacefully but in a relaxed, responsible and dignified way.
"The widespread consultation which took place was, I am convinced, a significant factor in reducing tension and avoiding the sort of confrontations we have seen in the past," he said.
Speaking after a meeting with the Taoiseach, Mr Ahern, in Cavan yesterday, the SDLP Assembly member for Upper Bann, Ms Brid Rodgers, said she was relieved that this year's Drumcree parade had not led to violence.
"The relief right across the community is palpable. I hope that the Orange Order will build upon the improved environment by responding fully to the requirements laid down by the Parades Commission."
Referring to the situation at Drumcree, she said there was no quick-fix solution.
"The issue is not just about getting a parade down the road. It is about establishing proper relations within a very divided community."