President Michael D Higgins says Irish society has work to do to improve the lives of Travellers.
He was speaking at an event to mark one year since the recognition of Traveller ethnicity.
President Higgins said that the goal should be full equality.
"I would love to see whoever is in Government in the coming years, if they have days like today, recalling the recognition of ethnicity, saying: 'We're going to start and put it right'," he said.
"And therefore that means it isn't a blame game now, it is a matter of making sure, for example, that every Traveller child, will have the rights of every other child, to participate in education right the way through."
Mary Stokes from Waterford Traveller Community Development Project says she doesn't feel like anything has improved over the past year: "If anything I feel they've gotten worse, maybe it's because we're more aware now of this step towards full equality with relation to our ethnicity being acknowledged."
"I'm sure it will be about 20 years before we'll see the benefits, where there will be equal employment, equal opportunities, education and accommodation.
Some of the action this morning from the Traveller Ethnicity Celebration at @RHK_Venue. Big thanks to @DeptJusticeIRL for their support. #ethnicitycelebration pic.twitter.com/VjlaWRXg5u
— Traveller Ethnicity Celebration (@TravellerEth) March 15, 2018