When a bishop leaves a diocese, he should give an honest assessment of what he has done and where he has fallen short, but mostly he should encourage people to follow the Lord, Pope Francis said.
The statement also said the Pope would not be issuing any statements, either during or after the meetings, "which will take place in absolute confidentiality".
Pope Francis had previous defended Barros, saying he had received no evidence of the bishop's guilt, and called accusations against him "calumny" during a trip to Chile in January. They did so in late April.
Pope Francis summoned the bishops to Rome for an emergency summit after receiving a 2,300 page report on the abuse cover-up scandal, which he had helped fuel.
"Pope Francis formally asked us for forgiveness, in his own name and on behalf of the universal Church", the three said in a statement released on Wednesday in Rome after their meetings with the pope.
The objective of the meeting, according to the Press Office of the Vatican, is to analyze the causes and consequences of the sexual abuses, of power, and of consciousness in Chile over the past few decades, as well as the mechanisms that led, in some cases, to covering up and serious omissions of the victims. As was announced on Saturday, Canadian Cardinal Marc Ouellet, head of the Vatican's Congregation for Bishops and of the Pontifical Commission for Latin America is taking part.
According a May 15 Vatican communique, Pope Francis met with the Chilean bishops today at 4pm local time, marking the first session of the May 15-17 gathering.
Both avoided giving a direct response regarding possible resignations of Chilean bishops.
The pontiff also acknowledged he made serious mistakes in his handling of the cases.
He concluded: "I think of the bishops, of all the bishops: may the Lord give the grace to all of us to be able to leave this way, with this spirit, with this strength, with this love of Jesus Christ, with this trust in the Holy Spirit".
"I've never seen him before in my life", Cruz tweeted. "Each person must decide this together with the pope", he said.
In a homily at his daily morning Mass on Tuesday, without specifically mentioning Chile, Francis said every bishop should know "when it's time to take his leave and step down".
In some way, the Pope said, Paul knows that he is going "towards trials, towards the cross and this recalls for us Jesus' entry into Jerusalem, doesn't it?" As a result, Paul exhorts "watch the flock; you are bishops for the flock, to keep the flock, not to climb into an ecclesiastical career", Francis explained.