Update 1.07pm: 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."
Earlier: Travellers call for dedicated centre to their highlight culture and history
Celebrations will take place today marking the anniversary of official State recognition of Traveller Ethnicity.
President Michael D Higgins is joining a special event this morning at the Royal Hospital Kilmainham in Dublin - that will feature Traveller music, theatre, storytelling and exhibitions.
The last Census showed there are currently over 30,000 Irish Travellers.
A leading Traveller activist said Martin Collins of Pavee Point that the community needs a national cultural centre to highlight its culture and traditions.
"There's a need for a dedicated space/centre that celebrates all things Traveller... and our culture and our history, in the same way that we have museums, heritage centres, and national galleries to celebrate Irishness," he said.
- Digital desk