Dr Hegarty said he hoped such meetings would address 'a dark period'
The Bishop of Derry has apologised to five people who suffered child abuse in Catholic Church-run institutions.
Dr Seamus Hegarty said: "For anyone to experience what they experienced is a cause of deep sorrow and shame.
"I am truly sorry that anyone should suffer such abuse in any institution operating where the spirit of Jesus Christ should have prevailed."
The delegation included people who were abused as children in the care homes of the Sister of Nazareth nuns.
The meeting at St Eugene's Cathedral lasted more than two hours.
The bishop said Tuesday's event was one of a number of meetings planned by the group with "church representatives throughout the north".
"It is my heartfelt hope that this series of engagements will help address the issues arising from the trauma experienced by innocent children in a dark period of our shared past," he added.
Bishop Hegarty apologised to the five victims of abuse
One of the delegates, John McCourt, said he believed Dr Hegarty's apology was heartfelt.
"It was daunting to talk about issues as sensitive and hurtful as this - we all had our preconceptions of how the bishop would react to us," he said.
"I was surprised at the degree of dignity and humanity he showed, and I genuinely believe his heart was open to us.
"He emotionally engaged with us for two and a half hours in what were some very deep conversations."
Mr McCourt said they did not raise comments made in December by Dr Hegarty, a month after a damning report into clerical sex abuse in the Dublin archdiocese, when he said some victims involved in legal action found "their experience in court much more traumatic for them than the original sexual abuse".