It has been learned Archbishop Martin travelled to attend a private wedding in the city.
But he also used the occasion to visit Cardinal Connell, who is recovering after falling last week, at the Pontifical Irish College.
The Archbishop urged his predecessor to reconsider his High Court attempt to prevent the Dublin Diocesan Commission of Investigation from examining files relating to his handling of complaints against paedophile priests.
During the visit, Archbishop Martin told Cardinal Connell he had received emails from victims of abuse who were very hurt at his court action.
"The Cardinal was in some pain and the discussion was brief," a spokesman for Archbishop Martin said.
"The Archbishop expressed his concern to the Cardinal that his decision to go to the High Court could have far reaching implications.
"Archbishop Martin is concerned that the hard work put in by many people, in the interest of the truth about the abuse of children by clergy, and in the area of an expanded church protection, could be overshadowed by the Cardinal's action."
Senior Church sources last night indicated Cardinal Connell's response will not be clarified until he has consulted his own legal team.
However, the gulf between the two senior Catholic prelates appeared to widen yesterday as Archbishop Martin instructed a separate set of lawyers to represent his interests, a move that signals the Dublin Archdiocese will also become party to the litigation.
Speaking earlier, the former Vatican diplomat admitted he was taken "by surprise" at Cardinal Connell's move to restrict access to diocesan files he had already handed over to the Commission.
"He simply called me and told me that his legal advisors had unanimously advised him to go to the High Court," Archbishop Martin said.
"He was not able to tell me the details of that, because that was a question that is still a little bit unclear, exactly what the nature of this case is."
Archbishop Martin said he hoped the legal action did not overshadow the work already done in the diocese to stamp out abuse.
"My hope is this is a single road block which we can overcome," he added. "I don't believe that this will be helped by polemics. Let's get obstacles out of the way and move back to what we always wanted."
Last week, following unanimous advice from his lawyers, Cardinal Connell secured an injunction against the inquiry to block it from examining some 5,586 of 66,583 documents given to it by Archbishop Martin.
Cardinal Connell claims the files are legally privileged.
Earlier yesterday, the High Court postponed the Cardinal's legal challenge until Monday.
The Commission undertook not to examine the documents pending the outcome of the full hearing.
The substantive hearing is expected to proceed next month.
Meanwhile, further indirect pressure for Cardinal Connell to soften his independent legal action came last night from the Primate of All Ireland, Cardinal Sean Brady, when he was accorded a state reception by Taoiseach Bertie Ahern at Dublin Castle.
Cardinal Brady refused to comment on Cardinal Connell's controversial court action.
But he reaffirmed all of Ireland's 26 senior bishops remain "united and determined to get to the truth" for the sake of the victims of clerical child sexual abuse, and for the Irish Church to get on with its placing of child protection safeguards fully in operation.
However, Cardinal Brady said he had no plans to meet Cardinal Connell to discuss the matter in person.
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