The Garvaghy Road Residents Coalition has called for an international mediator to be brought in to try to resolve the Drumcree parade dispute in Portadown.
Speaking after an 80-minute meeting with the Parades Commission, the coalition warned the dispute could take “months” to resolve.
The Orange Order wants to parade along the mainly-nationalist Garvaghy Road area on Sunday afternoon.
It is one of the most contentious parade routes in Northern Ireland.
The Parades Commission has begun a series of meetings as it weighs up whether to allow the march to go ahead this weekend.
Garvaghy Road Residents Coalition spokesperson Breandán Mac Cionnaith described the current mediation process on offer as “flawed”.
He said an international figure from “outside Ireland” was required.
Asked if he received any indication from the commission about which way their decision would go, he said he got none.
The Loyalist Communities Council (LCC) described its meeting with the commission as “frank but constructive”.
LCC Chairman David Campbell, who said the commission’s “credibility had long ago expired”, said it was “grossly unjust and partisan” not to allow the parade to take place.
Loyalist activist Jamie Bryson, who is acting as an adviser to Portadown District, said he welcomed that the residents coalition was prepared to engage in mediation but warned it must be a genuine attempt to find an agreement.
Bryson said: “The Portadown District will talk to anybody if they want to talk between now and the weekend to see if something can be worked out.
“The Portadown District stands ready to do that – but this cannot be used as a delaying tactic.”
SDLP leader Claire Hanna however said there was “no appetite” for the parade to take place.
“Residents do not want old wounds reopened, community relations damaged or further disruption caused. These are all factors the Parades Commission must take into consideration.”
Alliance also meet with the commission.
MLA Eoin Tennyson said the progress made around Drumcree since 1998 needs to be “preserved” and that efforts to jeopardise it were concerning.
“There are actors in the background, trying to stir division and reopen old wounds. They are picking at a scab with a chainsaw, they have no vision for our shared present or the kind of shared future we want to build,” he added.
