In a speech at Ulster University Campus in north Belfast, President Connolly acknowledged that across the island of Ireland there are “different aspirations for the future”, and an “unfinished story”.
She also met First Minister Michelle O’Neill and deputy First Minister Emma Little-Pengelly, which she described as “joyful and interesting and forward-looking”.
“Northern Ireland, without exaggeration, now represents a beacon of light to a world in how decades-long conflict can be resolved and reconciliation fostered and continued,” President Connolly said.
“In the world unfortunately that is ever more consumed with war and militarism, Northern Ireland’s lesson is increasingly important and increasingly significant and it is a lesson that we should all tell the world, that peace is normal and that war is not normal and that peace is possible.”
Ms Connolly said the Troubles had left “deep marks” on the region and many “continue to live with grief and pain every day”.
“It is the collective responsibility on all of us to address properly the needs and the questions of the families most affected, wherever they are, with integrity and a determination to deliver truth, accountability and justice for them and for society,” she said.
“As President, I give an absolute commitment that I will ensure, from my point of view, in my work, that all voices from all backgrounds are heard, regardless of gender, age, belief, ethnicity or nationality.”
She quoted Article Three of the Irish constitution, saying: “It is the firm will of the Irish nation, in harmony and friendship, to unite all the people who share the territory of Ireland in all the diversity of their identities and traditions.”
She said: “As President I look forward to playing my part in deepening relationships on this island.
“We won’t always agree and, in fact, life would be a very dull place if we all agreed.
“We will have different perspectives, which are crucial when we have dominant narratives in the world, now more than ever we need different perspectives and, of course, different aspirations for the future, and I want to acknowledge that publicly.
“All those perspectives and aspirations are legitimate, but I believe deeply that we are made richer by the different traditions on this island.
“I believe that the history and heritage of every single person and every community on this island has something that we can learn from.
“We did not and we do not live separate histories sent off from each other. We live and are living in an intertwined and unfinished story.
“For me, Irishness is as varied as those who identify with it in whole or in part.
“Our games, our music, our languages, and I emphasise, languages should never divide us, they are integral to this island’s cultural wealth. They are our shared treasures.”
Speaking in nearby Parliament Buildings later, First Minister O’Neill said she believed they were going to have a “very good relationship”, adding that she has invited Ms Connolly to attend the first Fleadh Cheoil na hÉireann in Belfast later this year.
The President’s official visit to Northern Ireland will continue on Thursday and Friday with engagements in Derry.