Further allegations have been made of sexual and physical abuse by monks at a former boarding school.
An investigation was launched after pupils of the Catholic Fort Augustus Abbey school told a BBC Scotland investigation they were molested and beaten by monks over a period of three decades from the 1950s.
Abuse was also carried out at Carlekemp, its feeder school in East Lothian, it is claimed. Both schools are now closed.
Five men said on the Sins Of Our Fathers documentary, screened last Monday, that they were raped or sexually abused by Father Aidan Duggan, an Australian monk who taught at Carlekemp and Fort Augustus between 1953 and 1974.
Fr Duggan died in 2004 but some of the abuse claims relate to men who are still alive.
The investigation follows a report in March by a former pupil of the abbey school, with officers liaising with law enforcement agencies across and outside the UK, Police Scotland said.
Detective Chief Inspector Pamela Ross said: “Further individuals were identified as part of the investigation and following recent media coverage, a further number of former pupils have come forward to speak to us.
“We understand that it must be very difficult to speak about such matters but if anyone has any information about this case, they are encouraged to come forward and report this to police. Any such reports will be directed to the inquiry team and investigated and dealt with very sensitively by trained officers.”
Meanwhile, one of Scotland’s most senior Catholics apologised to pupils during mass at Fort Augustus church.
Hugh Gilbert, Bishop of Aberdeen, said the claims are “bitter, shaming and distressing”.
He said: “We are anxious that there be a thorough police investigation into all this and that all that can be done should be done for the victims.”
But Christopher Walls, one of the former pupils featured in the programme, told BBC Good Morning Scotland that he is “less than impressed” with the apology and he is considering legal action.
“Surely they know that there was a problem of great extent. We’ve been complaining about it since 2010 officially, my brother and I. I’ve mentioned it to other clergy in between several times, always getting a ‘shushing’ response – ‘keep quiet about it and offer it up’ – presumably not to disturb the unity of the church.
“I think these are sins crying out for vengeance quite frankly and the response must be more vigorous and more directly concerned with me. I would like to have a response that puts me in the frame somewhere.”
Asked whether he is considering legal action, he said: “Ideally I’d like them to settle out … because it saves everybody a lot of problems and it also would make me feel a bit prouder of the faith I’ve been involved in all my life.”
The school was run by Catholic Benedictine monks and in the BBC programme Dom Richard Yeo, abbot president of the English Benedictine Congregation, apologised for “any abuse that may have been committed at Fort Augustus”.
Bishop Gilbert, 61, is the first senior Scottish Catholic to speak out. He has been Bishop of Aberdeen for around two years and the diocese covers much of the north of Scotland, including Fort Augustus.
The Church is reportedly planning to publish annual audits dealing with abuse allegations against Scottish clergy.