Frank Titas, a spokesman for the community, said its board of trustees delivered a letter to Lennon earlier this week outlining members' feelings.
Titas described the letter as "respectfully advising" Lennon that the community did not want to continue discussing the issues involved with the congregation, which worships on its own, away from Lennon and the diocese.
Robert Tayek, a spokesman for the diocese, said Wednesday that he was not aware of the community's letter to Lennon, who is out of town.
Lennon and trustees from the Congregation of St. Peter met just once in May, the first time they had come together since the bishop closed St. Peter Catholic Church, on Superior Avenue in 2010 as part of a downsizing of churches.
More than 300 parishioners then set up the nonprofit Community of St. Peter and rented space at East 71 and Euclid Avenue.
Titas said the congregation was surveyed about the meeting with Lennon, and the decision to break off talks soon followed.
"It became pretty clear that they were happy and comfortable and didn't really feel there was a need for a change,'' Titas said. "We'll continue full-speed ahead with what we're doing. We're not a parish that is in the Diocese of Cleveland.''
Dorothy Sadowski, a Fairview Park resident who is a longtime member of St. Peter, agreed: "I'm at peace with the decision. I didn't see any reason to continue. [The bishop's]
Titas declined to provide The Plain Dealer with a copy of the letter sent to Lennon.
In May, Lennon told members of the St. Peter community that Catholic worship outside the authority of the diocese is a violation of church teachings.
A report of the meeting, which was in a recent community newsletter, quoted Lennon as saying, ''joining in the liturgy at the community is not evil, but it is not an act in union with the Catholic church and was outside the authority of the Bishop.''
Last month, Sister Susan Clark, a member of the Sisters of Notre Dame, was told by a superior to stop worshipping with the congregation that severed its ties to the diocese.
A newsletter from the congregation reported that Clark was told by the religious order that she faced possible expulsion if she did not leave the congregation.
She had been the music director for the St. Peter congregation for years.
She moved with the community in 2010.
Titas said the responses to the survey of the congregation's members were received well before Clark made the decision to follow the instructions of her order.
In March, Lennon declared the Rev. Robert Marrone, the community's pastor, excommunicated, saying "Father Marrone's recent actions have been in direct defiance of the church's teachings and authority.''