Members of the Orange Order were among 200 guests at a reception to mark the Twelfth of July held by the President, Mrs McAleese, in Áras an Uachtaráin on Saturday.
President McAleese, who has been hosting the annual reception since 1998, invited a range of guests from both sides of the Border, including community representatives and development groups.
About 40 members of Orange lodges from the Republic's three Ulster counties, as well as Dublin, and Wicklow, were also present.
The President said some people at the reception may have had reason to be "fearful or distrustful" because of the legacy of politics and history, but she hoped their presence represented a new era in North-South relations.
"We see in you presence the kind of civility and generosity of spirit which we hope will in time transform relationships on this island, making good friends of those who look at things differently, taking nothing from each other but only adding to our respective store of friendships and happy memories," she said.
"We gather here today a new generation of Jacobites and Williamites in a new era seeking to comprehend and befriend each other, so that the generations to come will not know the waste of violence, the hurt of contempt."
The reception, the first accorded to Orangemen by an Irish President, forms part of Mrs McAleese's "bridge-building" policy.
The guests were entertained by the traditional musician David Hammond, Celtic folk guitarist Arty McGlynn, and fiddle player Nollaig Casey.
President McAleese said both communities had traditions, such as musical heritage, which should be shared.
"They each have their own genius, their own story, and the story of this island is incomplete if any one of them is missing," she said.
"Without compromising those things we hold dear, we have an obligation and an opportunity to build a culture of respect for difference and of relaxed curiosity about what we have in common as well as what separates us. To do that, we need to get to know one another and that is what today is about," she said.
