Police came under attack during three nights of rioting in Belfast earlier this week
Hopes have risen that a major loyalist rally in Belfast later this month will pass off without trouble.
It followed an unprecedented apology by the Royal Black Institution to Catholic clergy and parishioners in the city centre where band members ignored a ruling not to play music outside their church during a march last month.
Sinn Fein's Gerry Kelly said: "It is a step in the right direction."
Northern Ireland First Minister Peter Robinson and Deputy First Minister Martin McGuinness have been heavily involved in talks to find some sort of agreement in advance of a huge rally by another of the loyal orders, the Orange Order, in Belfast on September 29 when thousands are expected on the streets.
More behind-the-scenes discussions are due to take place and may involve community representatives in north Belfast, where three nights of serious rioting earlier this week left scores of police officers injured. The Protestant paramilitary Ulster Volunteer Force has been accused of orchestrating the trouble.
A statement by the institution's sovereign grand master William Farr said: "We have always had good lines of communication with the Roman Catholic Church and we would intend to continue to maintain and consolidate these, away from the public gaze.
"The sense of injustice and hurt felt by the members of the Royal Black Institution is focused on the Parades Commission and its irrational and often irresponsible determinations. The Royal Black Institution is founded on Christian principles and all of our processions are to and from an act of worship.
"Our institution is determined to play its full part in civic society and make Northern Ireland a peaceful and prosperous part of the United Kingdom where cultural diversity is respected."
All sides believe the apology could clear the way for a resolution to the issue of the big march to mark the anniversary of the signing of the Ulster Covenant. It was immediately welcomed by the priests of St Patrick's Church.
Nelson McCausland, a Democratic Unionist Party minister in the power-sharing executive at Stormont whose constituency includes the loyalist area at the centre of the violence, said: "It is a sign of maturity."