Respect is the key to progress, Northern Ireland's First Minister said tonight.
In a speech at an event celebrating the role of the GAA in peace building, Peter Robinson also claimed that communications between unionists and nationalists had to be improved.
He said: "What I want to see is a society where there is respect for the constitutional reality but also for constitutional aspirations.
"Respect for another person's culture and also for their right to live in peace. Respect for the lawful authority of the state and for the individuals within it."
The DUP leader was guest speaker at the Co-operation Ireland gala dinner at Queen's University in Belfast which was organised to acknowledge the sports association's efforts to forge better community relations.
His attendance, which he admitted would have been unimaginable a few years ago, will be seen as the latest in a line of symbolic gestures by ministers within the DUP/Sinn Fein-led power-sharing executive aimed at showing respect for each other's sporting traditions.
DUP members have attended a number of GAA matches in recent years - with Mr Robinson notably joining Deputy First Minister Martin McGuinness at last year's McKenna Cup final in Armagh - while Sinn Fein Sports Minister Caral Ni Chuilin has watched a Northern Ireland international football match at Windsor Park in Belfast.
Last Friday Mr Robinson and Mr McGuinness sat side by side to watch Ulster Rugby defeat Leicester Tigers in their Heineken Cup clash at Ravenhill in Belfast.
In a possible reference to the dissident republican murder of a man in north Belfast last week and the shooting of a 24-year-old woman by loyalist paramilitaries in east Belfast, Mr Robinson said he had no hesitation in condemning such actions.
He said: " An a la carte approach to the rule of law is not a basis for building the kind of peaceful democratic society that we all want to have.
"I make no distinction whatsoever between shootings by the UVF and shootings by dissident republicans and I have no reservation, mental or otherwise, in condemning all such activity.
"Nor do I make any distinction between terrorism now and terrorism in the past. It was and is all wrong. Cherry-picking on these matters is not credible."
He also appeared to take a swipe at republicans over the staging of a controversial IRA commemoration parade in Castlederg, Co Tyrone in August and plans to honour Shankill Road bomber Thomas Begley this weekend.
"It is also wrong to honour and extol those who participated in such activities," added Mr Robinson.
Political relations at Stormont and community tensions at interface areas in Belfast have been strained following some of the most difficult months since the signing of the Good Friday peace agreement in 1998.
However, Mr Robinson said he was hopeful that Dr Richard Haass, the US diplomat drafted in to resolve three of the most contentious issues: flags, parades and the past, could deliver.
He said: "I hope that the Haass process this autumn can deliver, but ultimately it will be people's attitudes that will matter more than institutions or regulations.
"Many of the problems that we face could be solved with goodwill and a generosity of spirit that has not always been present.
"What is required is that each one of us should be as mindful of our responsibilities as we are of our rights."
The Co-operation Ireland event is essentially the second half of its celebration of the GAA's efforts, having staged another gala dinner at Trinity College Dublin earlier this year.
The peace building charity has also held events for soccer and rugby in the past.
Secretary of the GAA's Ulster Council Danny Murphy described the presence of the DUP leader at the dinner as another "significant step" on the way to improving community relations.