Cardinal Connell said a Church of Ireland liturgical reception held in his honour in Dublin last night was the most special event he had attended since becoming a cardinal.
The reception at Christ Church Cathedral was hosted by the Church of Ireland Archbishop of Dublin, Dr Walton Empey, Dean John Paterson, the cathedral board and the chapter.
"I like to look on this building as a sign that beckons us towards a new future for our divided Christian communities today. Is it too fanciful to look on its beauty, rising over the Liffey and the quays, as testimony in stone to a time when all our ancestors worshipped together, or to hear in the music of its bells a call appealing to us to remain faithful to Christ and to his prayer that we all might be one?" the cardinal asked.
He recalled the friendship between his predecessor, Archbishop Kevin McNamara, and the former Church of Ireland archbishop of Dublin, Dr Donald Caird. "One of the last phone calls made by Archbishop Kevin was one to Dr Caird, to say goodbye to his friend and `to thank you for your friendship and kindness'," he recalled.
Addressing Archbishop Empey, the cardinal continued: "Such was the tradition and atmosphere of undemonstrative but genuine warmth and caring personal friendship that your grace and I - and indeed, our clergy and laity - inherited from those who have gone before us.
"It is something that does not make headlines but, as your grace and I know only so well, it is very real and very precious to us. It is a legacy that you and I, and all of us, have been doing our best, not only to preserve but, where possible, to expand and build up."
The cardinal said he took heart from the evening as "a sign that the ecumenical soil in Dublin remains fertile and that our own efforts, modest though they may be, have received a blessing from God".
He prayed "that this celebration may renew our hearts and boost our determination to loosen afresh the ecumenical soil in our patch of the vineyard."
Earlier, Archbishop Empey said: "Dublin has rejoiced in your elevation. Speaking for myself and for the dean and chapter of this ancient cathedral body, it is our delight to be a part of these celebrations and to greet you in the name of the Lord."