DUP leader Peter Robinson is to hold talks with both sides in the dispute over the Drumcree Orange parade.
Orangemen have been banned since 1998 from going down the mainly nationalist Garvaghy Road in Portadown after their annual march from Drumcree church.
This year's parade takes place on Sunday, and faces similar restrictions.
Mr Robinson said he had invited both groups to separate meetings aimed at "enabling progress to be made, leading to a resolution of this matter".
"By demonstrating a common-sense approach, I am certain that we can find a way through on this issue," he said.
"I will do all I can to help progress this matter to a consensual conclusion but I would be equally content if, in the preliminary discussions, the two parties agree on some other approach or arrangement which might reach the outcome that everyone in Portadown and indeed throughout Northern Ireland wishes to see."
In a statement, the Garvaghy Road Residents Coalition said a meeting would take place next week.
"We will use the opportunity to put forward the views of the nationalist community in Portadown - views which have not been heard before at such a senior level within the DUP.
"Past experience has shown, however, that partisan political interventions by senior political figures have served no useful purpose in the past.
"Nevertheless, we will not seek to pre-judge either the purpose or the outcome of this planned meeting by speculating on the reasons behind it."
Portadown district master Darryl Hewitt said he hoped they could get a resolution to the impasse.
He criticised the Parades Commission for "failing to deliver" on their willingness to hold face-to-face talks with residents.
"It needs somebody to inject fresh impetus into the situation, and if it's the first minister, so be it," he said.
Mr Hewitt said they held talks with Mr Robinson last month.
Before 1998, attempts to ban the parade from going down the road resulted in loyalist rioting both in Portadown and across Northern Ireland.
However, when the 1998 march was forced through the Garvaghy Road it sparked republican rioting.