Speaking at London's Westminster Cathedral, he acknowledged the "immense suffering" inflicted by ministers - echoing comments made to reporters on board his plane as he flew into Britain on Thursday morning.
Addressing the faithful at Holy Mass, he said: "I think of the immense suffering caused by the abuse of children, especially within the Church and by her ministers.
"Above all, I express my deep sorrow to the innocent victims of these unspeakable crimes, along with my hope that the power of Christ's grace, his sacrifice of reconciliation, will bring deep healing and peace to their lives.
"I also acknowledge, with you, the shame and humiliation which all of us have suffered because of these sins."
Focusing on those who suffered at the hands of ministers, he added: "I invite you to offer it to the Lord with trust that this chastisement will contribute to the healing of the victims, the purification of the Church and the renewal of her age-old commitment to the education and care of young people.
"I express my gratitude for the efforts being made to address this problem responsibly, and I ask all of you to show your concern for the victims and solidarity with your priests."
His comments follow his strongest admission to date of failings in the way the abuse scandal was handled.
On his flight into Britain, he said the Catholic Church had not dealt with abusive priests decisively or quickly enough and said its top priority now was helping victims heal and regaining their trust in the Church.
Opening his sermon at the main Catholic church of England and Wales, the Pope thanked those present for their "warm reception".
He added: "I am especially happy that our meeting takes place in this Cathedral dedicated to the Most Precious Blood, which is the sign of God's redemptive mercy poured out upon the world through the passion, death and resurrection of his Son, our Lord Jesus Christ."
And he welcomed Dr Rowan Williams saying: "In a particular way I greet the Archbishop of Canterbury, who honours us by his presence."
During the 13-minute address, Pope Benedict spoke of the "insights and teachings" of Cardinal John Henry Newman, the Victorian intellectual and preacher who will be beatified by the Pontiff tomorrow in Birmingham.
He said: "May the profound ideas of this great Englishman continue to inspire all Christ's followers in this land to conform their every thought, word and action to Christ, and to work strenuously to defend those unchanging moral truths which, taken up, illuminated and confirmed by the Gospel, stand at the foundation of a truly humane, just and free society.
"How much contemporary society needs this witness! How much we need in the Church and in society, witnesses of the beauty of holiness, witnesses of the splendour of truth, witnesses of the joy and freedom born of a living relationship with Christ!"
And he said one of the "greatest challenges" facing Catholics today was how to "speak convincingly of the wisdom and liberating power of God's word to a world which all too often sees the Gospel as a constriction of human freedom, instead of the truth which liberates our minds and enlightens our efforts to live wisely and well, both as individuals and as members of society."
He added: "Let us pray, then, that the Catholics of this land will become ever more conscious of their dignity as a priestly people, called to consecrate the world to God through lives of faith and holiness."
And he said: "The more the lay apostolate grows, the more urgently the need for priests is felt."
Concluding his sermon, the Pontiff urged listeners "once more to look to Christ," adding: "I pray that in doing so, you may join the ranks of faithful believers throughout the long Christian history of this land in building a society truly worthy of man, worthy of your nation's highest traditions."
Earlier this morning, the Pope met Prime Minister David Cameron. He arrived at Archbishop House, behind Westminster Cathedral in central London at 8.40am followed 15 minutes later, by the Prime Minister.
It is the first time the two men have met since the Pope arrived in the UK as Mr Cameron was attending his father's funeral yesterday when the Pontiff addressed MPs in Westminster Hall.
Pope Benedict XVI's meeting with Mr Cameron comes as six men remain in police custody after they were arrested over an alleged plot to attack him.
Five street cleaners were arrested yesterday morning as armed officers swooped on a depot as they prepared to start their shift. Hours later a sixth man was arrested at a home in north London.
The Pope arrived in a BMW rather than the Popemobile, wearing a white gown and red shoes.
The Archbishop of Canterbury Dr Rowan Williams, arrived shortly after 9am.
Deputy prime minister Nick Clegg arrived to meet the Pope, accompanied by his wife and children.
Mr Cameron then left Archbishop's House after a 20 minute audience, at which point acting opposition leader Harriet Harman arrived.
As she left after her meeting, she said: "I was very pleased to express the welcome to the Pope on his visit to this country as leader of the opposition and on behalf of the Labour Party.
"We talked about the many struggles for social justice that the Catholics and the Labour party have struggled on together.
"We talked about the challenges that still remain here and abroad.
"We reflected on the long, close connection between - and the leading role played by - Catholics in the Labour Party over many decades and I wished him well for the rest of his visit."
She did not say whether they discussed the issue of gay adoption within Catholic adoption agencies.
Former prime minister Tony Blair, a catholic convert, and his wife Cherie arrived at the Cathedral ahead of this morning's mass.
Mr Blair stood to admire a long line of priests from England, Wales and Scotland who had gathered alongside the cathedral, preparing to celebrate the mass.
Several of the priests, who appeared in excitable mood, waved at the Blairs and pulled out pocket cameras to take photographs.