"The way we have treated our brothers and sisters from the LGBTIQ community has brought them to tears and disgraced too many of us," Gregory said in a speech, the text of which was published by the portal"Outreach" on Tuesday.
The cardinal was speaking to members of the LGBTIQ community in a church in Washington.
"I apologise from the bottom of my heart for the pain that has led to the loss of so many of our family members who belong to God no less than I do," Gregory continued.
He apologised not only for those "whose actions in the past have scandalised and wounded these men and women", but also for his own lack of courage to give hope to those affected.
Climate of division
In his remarks, the former Archbishop of Washington lamented an ideological divide in the Church. Catholics on both sides of the spectrum had "heaped vicious and cruel condemnations" on anyone who did not see the Church as they did.
In such a climate, the work of evangelisation becomes "even more difficult and unpleasant".
According to Gregory, he is also concerned that more and more people are turning their backs on the church.
In addition to scandals, the reasons for this include "insensitive pastoral encounters with clergy" and "a callous attention to the spiritual needs and aspirations of people based on their gender identity".
For him, the question is how the Church and he himself could fail to "effectively witness to Christ so that my sisters and brothers are strengthened in their faith instead of abandoning it".
Cardinal Wilton Gregory (77) was Archbishop of Washington until the beginning of this year; on 6 January, Pope Francis accepted his age-related resignation.
At the same time, the head of the Church appointed Cardinal Robert W. McElroy, previously Bishop of San Diego, as Wilton's successor.