The chair of the Parades Commission has said she and her colleagues do not intend to resign.
Professor Evelyn Collins was speaking two days after a court case highlighted mistakes made by the commission in its ruling on last month's planned parade by the Orange Order to Drumcree church in Portadown.
"We will work hard to regain the trust of all sections of the community," she said.
Speaking to Good Morning Ulster, Collins added: "Rather than resign, the commissioners and I are very committed to fulfilling our responsibilities under the legislation, to completing our terms of office and to addressing and fixing the problems that have been identified."
She also said they "accept criticisms that have been made".
The Orange Order has confirmed it intends to apply for another Drumcree parade in the coming days and a "significant date" in the calendar may be chosen for the parade.
Nigel Dawson, Portadown District Master said the Orange Order was agreeable to mediation with Garvaghy Road residents but questioned whether they wanted to engage in discussions.
A representative of a residents' group said there would be no point in discussions if the Orange Order had a "pre-determined outcome".
The Northern Ireland Secretary of State met the Parades Commission chair on Wednesday.
A Northern Ireland Office (NIO) spokesperson said Sir Chris Bryant expressed "serious concern over the issues highlighted" in the judgement during the meeting.
Sir Chris has asked for written assurances that the commission's decision-making processes are "fair and robust", that they act "independently and impartially" and that they have a plan to "enhance public confidence".
When did the Drumcree dispute begin?
In 1998, the Parades Commission ruled that the Orange Order should not march down Portadown's Garvaghy Road on the end leg of its annual march from Drumcree Church.
It was a move that ultimately led to a decades-long parading dispute, sparking some of the most serious public disorder in Northern Ireland's history.
Stand-offs continued in subsequent years as members of the Order walked to police barricades in protest at the restrictions. Protests were also held by residents living along the Garvaghy Road.
The High Court was told on Tuesday that the commission conceded the case last week and requested the court quash its determination before a full hearing.
The commission conceded a procedural error in how it dealt with the annual application for permission to walk along the Garvaghy Road.
Not all six members of the public authority had signed off on the final determination before it was issued last month.
Lawyers representing the local Orangeman claimed the commission's latest decision unlawfully breached his rights to freedom of belief, expression and peaceful assembly under the European Convention on Human Rights.
Lawyers for the applicant also argued that Garvaghy Road residents had refused talks with the Orange Order and the commission breached legislation by making it "a pre-requisite to a parade".
The Parades Commission said it "welcomes scrutiny and accountability".
What has been the reaction?
The Northern Ireland secretary said on Tuesday that it was "really important that the Parade's Commission carries the respect of all communities in Northern Ireland, otherwise it simply can't function".
Sir Chris said he had not read the "precise terms" of what has been said, but added that he was "concerned that it looks as if the Parades Commission have not got things right here".
The Grand Orange Lodge of Ireland said the ruling made "the position of the current commissioners untenable".
Breandan Mac Cionnaith of the Garvaghy Road Residents' Coalition said people "had pointed out their concerns, their worries" at the meeting with O'Neill on Wednesday.
"I think people also have to be realistic, it is 28 years since the last Orange march ever came down Garvaghy Road and it has already been said who wants to open that can of worms again?"
He said the Orange Order parade "finished" in 1998 and it "will not be repeated".
"No more marches," he added.