The 22-page letter has one paragraph on sexual abuse
He said these brothers had succumbed to "the most grievous form of evil at work in the world".
Just one paragraph in the 22-page letter was devoted to the issue and the word paedophilia was not mentioned - but it is still the first time the Pope has addressed sexual abuse since a major paedophile scandal engulfed the Roman Catholic Church in the United States.
Other cases of sexual abuse and harassment involving the clergy have also recently come to light across Europe, and in Australia.
Last year the Pope sent an apology by e-mail for a string of injustices committed by clergy in the Pacific nations, which included priests and missionaries forcing nuns to have sex and then abortions.
In this most recent letter, he said the church "showed its concern for the victims".
The Vatican has frequently been criticised for its slow response to accusations of sexual misconduct, and its tendency to regard such reports as attempts to discredit the Church.
Costly claims
The scandals are also proving expensive.
In January, the Catholic Church in Ireland agreed to a $110m payment to children abused by the clergy over decades. More than 20 priests, brothers and nuns have been convicted of molesting children.
The US archdiocese of Boston has agreed to pay between $15m and $30m to scores of people to settle claims that a priest sexually abused them when they were children.
The now defrocked John Geoghan has already been sentenced for up to 10 years for sexually molesting a young boy, and as many as 200 alleged victims have accused him and other Boston-area priests of sexually abusing them.
The case has seriously tarnished the reputation of Cardinal Bernard Law of Boston, whom the Pope is said to hold in high esteem.
According to the Boston Globe newspaper, which carried out extensive investigations, Cardinal Law knew about John Geoghan's behaviour but just moved him from parish to parish, without keeping him from children.
Even closer to home, the Polish-born Pope is reported to be particularly saddened by sexual abuse allegations against Monsignor Juliusz Paetz, archbishop of Poznan.
Archbishop Paetz denies that he sexually abused seminarians and priests.