Speaking at Queen's University, Belfast on Thursday evening at the Co-Operation Ireland dinner, Mr Robinson acknowledged the significance of his appearance.
"Not so many years ago it would have been unimaginable that I would have been invited to speak at an event of this kind - or that I would have accepted," he said.
"Thankfully the world has moved on. We are all on a journey. Although I think we each recognise that there is still some distance to travel.
"For my part I want to see my party reaching further out further in the years to come and I am certain that the GAA leadership will want to do the same."
It is a testament to the progress that we have all made that tonight we can acknowledge the GAA's role in peace-building by inviting a First Minister from the unionist tradition to the lectern.
He said the GAA's scrapping a ban on members of the security forces 12 years ago was a "harbinger of things to come".
"Last week I opened a newspaper to see a photograph of my colleague Nelson McCausland playing Gaelic Football," he said.
"That really does show that all things are possible! Don't think for one minute that I take any of it for granted. I believe that the hand of reconciliation needs to be extended by all of us and at every possible opportunity."
The DUP leader spoke on the importance of a legacy of peace-building.
"Addressing the divisions we have lived with for past generations for the benefit of the next generation, is the greatest legacy that any of us could leave," he said.
"Of the many challenges that we face in Northern Ireland today none is more important than improving community relations and building a shared and united future for all our citizens.
"If we get that right then there can be no more secure foundation for growth and economic prosperity. But if we get it wrong it has the potential to destabilise our society and prevent us from realising the potential that exists."
The Investment Conference held in Belfast last week demonstrated "partnerships in action" according to Mr Robinson and was a sign of what he and deputy First Minister Martin McGuinness can achieve when they work together.
But the First Minister also addressed remaining challenges, stating: "dangers that can arise if we do not tackle the legacy of the past and strive to build a better future".
He deemed the funeral of Ronan Kerr, a Catholic PSNI officer killed by a dissident republican car bomb, as a symbol of the changes within society.
It wasn't popular with everyone in my constituency that I went to the McKenna Cup Final or attended a funeral requiem mass, nor was it popular with everyone in the deputy First Minister's community when he met with Her Majesty the Queen. But those were all the right things to do.
He added that these gestures "can have a significant impact and over time can help change perceptions and responses".
Mr Robinson told those at the dinner that he wanted to see a "community united, with shared goals and dreams".
"I want to make progress not just for that section of the community from which I come but for everyone who inhabits this place that we all call home," he said.
"But I know that to achieve that vision we must all work together."
He added: "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."
He added that he hoped the Haass talks would deliver progress but added that "ultimately it will be people's attitudes that will matter more than institutions or regulations".
He also condemned terrorist activity on both sides.
"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," he stated.
"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."
Mr Robinson, who dedicated his 2011 assembly election win to Ronan Kerr, concluded his speech with a tribute to him and the GAA.
"His death was a tragedy for all of us - his family and friends, for the GAA, for the police and for the wider community, but out of it came a unity of approach which showed that so much more unites us than divides us," he said.
"We have all more work to do and more challenges to overcome. In all that I do I will continue to endeavour to make sure that we can become one shared and united community. For despite all of our difficulties and setbacks along the way I believe that this is the desire of the overwhelming majority of our people.
"That is why I am publicly acknowledging the contribution that the GAA has been making towards this goal and I am confident that the work the organisation has done, and continues to do, will play a very significant role in the years to come in building a better and brighter future."