Earlier in February, the pontiff said sorry to those abused in Catholic children's homes in Ireland, saying he shared public "outrage and shame" over the scandal.
He was criticised for not meeting survivors face-to-face, however.
Helen Holland, a 51-year-old leading figure in several survivors' groups, has accused Church authorities in Scotland of continuing to fail to acknowledge the harm done to generations of children.
She wrote to the Pope: "I know you have apologised to other countries where citizens suffered abuse within the church, but in Scotland the attitude of the church to date has been one of denial and indeed blaming the actual survivors of abuse."
Holland continued: "It is not acceptable for abusers or institutions to be allowed to hide behind either the collar or indeed the habit. I, as a child baptised into the Catholic Church, beseech you to address the pain still suffered by adult survivors."
She concluded: "I ask you to lead by example and apologise to the survivors of abuse in Scotland in the same way you have done in other countries. It is never too late for the healing process to begin. I believe God's love and compassion can break down even the strongest barriers."
Holland has described years of serious sexual and physical abuse at a children's home, Nazareth House in Kilmarnock, run by nuns and priests, reports Scotland on Sunday newspaper.
For ten years she has waived her right to anonymity as she worked for support and campaigning groups for fellow victims, including Survivors Scotland.
Cardinal Keith O'Brien of Edinburgh has apologised "unreservedly" to abuse victims. But Holland, still a convinced Christian, and other campaigners, want to see a change of heart on the issue right through the church and its various orders.
A spokesperson for the Catholic Church in Glasgow said: "The Church in Scotland has been at the forefront of child protection practice and has a robust policy in place across every parish and Church institution in the country to prevent the sexual abuse of children, which, as the Pope recently stated, is an abominable crime."
The Vatican did not offer a response to Scotland on Sunday over Helen Holland's appeal.
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