Travellers still "confront enormous discrimination" at many levels of Irish society, Minister for Health Mary Harney has said.
Speaking at an event in the National Gallery in Dublin today to mark the start of Traveller Focus Week, Ms Harney said: "This State has a long way to go to create the kind of society where Travellers can reach their full potential.
"Although some Travellers were involved in criminality - similar to a section of the settled community - the vast majority were law-abiding citizens," she said.
The theme of the week this year is "participation" - focusing in particular on Travellers' contribution to Irish art, music, culture and society.
The National Action Plan Against Racism - which is funding several events this week - has published a calendar of Louis le Brocquy paintings known as the Tinker Series.
The artist, who recently celebrated his 90th birthday, attended the event with his wife and son. He said: "Travellers had their own traditions, their own pride, their owns ways and their own strict morality.
"They have been prejudicially excluded by our settled society, yet they belong to us - they are a variant within us."
Director of Pavee Point Travellers Centre Ronnie Fay said: "Traveller participation in Irish society has long been overlooked."
"The focus on Travellers is all too often a negative one; this week gives us the opportunity to celebrate and value the very positive elements and contribution Travellers have made to the cultural and artistic life of this island."
She said: "There is another side to Traveller life that rarely gets portrayed, Travellers living their everyday lives and contributing to Irish society. That's what we are focusing on at this launch," she added.
Ms Fay criticised an opinion article in today's Irish Timeswhich she said had nothing positive to say about the Travelling Community and focused solely on anti-social issues.
She claimed the article essentially blamed Travellers for the situation they find themselves in and this was particularly disappointing from a newspaper which she said had long highlighted the inequality faced by Travellers.