Unionist leaders are to meet with the Secretary of State next week over their call for an inquiry into parades.
The Orange Order will also be part of the discussion.
They are expected to seek answers from Theresa Villiers on whether she will grant a commission of inquiry to examine a contentious march in north Belfast and the wider parades issue.
Hopes that the impasse can be resolved have heightened after the most peaceful Twelfth period in years.
Unionists and Orange Order leaders are demanding the Parades Commission is scrapped, and pledged a "graduated response" in the wake of a ruling banning Ligoniel lodges from returning along a stretch of the Crumlin Road.
Although Saturday's return leg passed off peacefully, the issue has still to be permanently resolved.
At a Press conference last Thursday unionist leaders hinted their support for the political institutions could be under threat unless Ms Villiers agrees to an inquiry. Yesterday DUP deputy leader Nigel Dodds refused to say if future steps of the graduated response had been decided.
Mr Dodds said the action would be "proportionate" and a reaction to how the situation develops. "The unionist leaders will make their announcements... as and when necessary," he told the BBC. Pressed on the potential consequences for the institutions, Mr Dodds warned against jumping too far ahead.
The North Belfast MP said a peaceful Twelfth must lead to greater tolerance and respect for the unionist culture. He said efforts would continue to try and resolve the parades dispute.
"In the aftermath of a very, very peaceful Twelfth, our work is only starting now in terms of the high level political engagement, and it's a furtherance of the work that has been going on on the ground – day by day and week by week – by people who have worked very hard to keep tensions low and to try and make progress," he added.
Residents' groups in Ardoyne called on the Orange Order to engage in talks about future marches on the Crumlin Road.
Joe Marley from Crumlin Ardoyne Residents Association said: "I think the Orange need to re-engage with local residents. I think we need to change the attitudes going into talks.
"I think what happened at the weekend was a positive move and I think we need to build on that, grasp the nettle with both hands."
Dee Fennell from the Greater Ardoyne Residents Collective said it would always be opposed to a return parade along the Crumlin Road by Ligoniel Orange lodges. "What we all need to do is sit down and make the alternative route viable," he said.
Story so far
Saturday's Twelfth was the most peaceful in years. The focus had been on the return leg of a feeder parade banned from passing the Ardoyne shop fronts, but it ended with no repeat of the violence of previous years. The largely peaceful Twelfth followed pleas from unionist leaders and senior Orangemen, however the wider issue of parades and marches in contentious areas has still to be resolved.