In a statement, the hierarchy said they welcomed Burma’s pro-democracy leader in the light of the continuing links between the Irish Church and the Church in Burma.
The Burmese pro-democracy leader is visiting Europe for the first time since 1988. She was held under house arrest or imprisoned in Insein jail in Rangoon, for 15 of the last 24 years.
She was finally released just last November.
Trócaire supports projects in Burma, while a number of Irish Columbans are buried in the country as the order had a missionary province in the northeast of Burma until they were prevented from working there in the 1960s by the military dictatorship.
The Columbans, in conjunction with the Diocese of Meath, continues to support education projects for disadvantaged children in the two dioceses where they previously had a presence.
Last week, Archbishop Grawng of Mandalay attended the 50th International Eucharistic Congress in Ireland.
Daw Suu Kyi was presented with the Amnesty Award at the Bord Gáis Energy Theatre on Monday evening as the Electric Burma concert was held in her honour.
The award was announced at a U2 concert in Dublin in July 2009 but Daw Suu Kyi was still under house arrest. U2 dedicated their world tour in 2009 to highlighting her plight and their hit, Walk On is dedicated to her.
When she was awarded by Freedom of the City of Dublin in March 2000 along with U2, her son Kim accepted it on her behalf. On Monday evening she was finally able to sign the Roll of Honour for Freedom of the City of Dublin at the invitation of Lord Mayor Andrew Montague and she made a short address to a crowd gathered to honour her.
She later flew to the Britain for a four-day visit where she has friends and family.
She lived in Oxford with her husband Michael Aris, before she became involved in 1988 with the pro-democracy movement in Burma. Her husband later died in March 1999 and the Burmese military junta refused his dying wish to see her one last time.
Prior to her arrival in Ireland, Aung San Suu Kyi was presented with the Nobel Peace Prize on Saturday, which she was awarded twenty-one years ago in 1991.
Welcoming her to Ireland for her six-hour visit, Tánaiste Eamon Gilmore told her the Irish Government pledged support for her efforts and he described her election to parliament as bringing about a new era of peace, democracy and human rights.
“Ms Suu Kyi is enormously admired in this country and her visit here is something which we have long hoped to see,” the Tánaiste said.