Ulster Unionist leader Sir Reg Empey has called for a "global solution" to the issue of contentious parades.
The Order had been linked to the party for 100 years
Sir Reg was speaking after holding talks with the head of the Orange Order, Robert Saulters, in Belfast.
He said it was up to the Order to decide if it should talk to nationalist residents groups on the issue.
Mr Saulters said the policy was not to talk to groups "fronted by IRA/Sinn Fein", but it could change when the Order's hierarchy meets in September.
He also denied his statement last week amounted to criticism of members of his own institution in Londonderry and west Belfast for engaging in dialogue with residents.
The Ulster Unionists had said Wednesday's meeting was arranged to explore how the new party leadership and the Orange Order could work together in the future.
Sir Reg said it was necessary to get "an overall appreciation of the parades issue "rather than have annual disputes over a whole series of different parades".
He said: "Many people find themselves under severe pressure in different localities. People at interfaces, their lives are turned upside down and there's a whole issue of rights and culture involved in this.
Sir Reg Empey led a delegation to meet the Orange Order leader
"We're interested in not seeing issues left simply to local circumstances.
"We believe that instability has been created each summer and we want a global settlement, in other words that there's a general understanding right across the community, a consensus into how these issues are going to be specifically dealt with."
The meeting involved other senior Orange officials and a UUP delegation comprised of David McNarry, Tom Elliott, Ken Robinson, Danny Kennedy and Michael Copeland.
In March, the Orange Order formally cut its links with the UUP, ending 100 years of historical ties.
At the time, the Order said because of restructuring within the party, it would have had to make "impracticable changes" to its constitution.
The links between the Ulster Unionists and the Orange Order dated back to a time when there was only one unionist party, but many Orangemen now support the DUP.
The UUP had refused to sever its ties, though the Order's influence had been greatly reduced in recent years.