Four years ago, a methodical search for a new place of worship led a group of gay Roman Catholics to the Rev. John Unni, the youthful priest at St. Cecilia’s Church. The search committee was blunt: Would the priest accept an influx of gay and lesbian parishioners?

“He told us, ‘All are welcome,’ ’’ said John Kelly, now head of the St. Cecilia Rainbow Ministry.

Kelly and other parishioners credit Unni with managing the merger of the predominantly gay congregation from the Jesuit Urban Center, which closed in 2007, and with keeping gays and lesbians in the Catholic Church, despite the uneasy balance between the church’s message of love for all and its strict doctrine against gay relations.

Father John, as his parishioners call him, says he is trying to live the words of Jesus Christ, as he has seen them lived out.

Unni was 16 when his father died. The St Theresa Parish community in his hometown of North Reading responded with meals delivered to the family’s door, with rides to practices and rehearsals and whatever help they could offer a broken family.

“People lived out the Gospels,’’ Unni, 49, said in an interview yesterday evening. “That’s when I learned what church was.’’

He said the response from his hometown was “the total opposite to the hateful reaction’’ that Unni and St. Cecilia have received recently from some conservative critics over the church’s plan to hold a June 19 Mass under the theme, “All are Welcome,’’ to commemorate Boston’s Gay Pride Month.

“All we’re trying to do is welcome a group that has been marginalized,’’ he said.

Critics have accused the church, and Unni, of celebrating behavior the church opposes. Those critics “are not about hate or lack of acceptance of people with same-sex attractions,’’ wrote blogger Joe Sacerdo, who has written extensively on St. Cecilia’s plans.

“The Catholic Church believes sex between men and men, or sex between women and women, is morally wrong and sinful. Period.’’

Last week, the archdiocese stepped in and postponed the “All are Welcome’’ service, saying it gave the impression that St. Cecilia’s supported the annual Gay Pride celebration.

Unni addressed the controversy during his homily Sunday, saying parishioners “are welcome here, gay or straight, rich or poor, young or old, black or white.’’

“Here,’’ he said, “you all can say, `I can worship the God who made me as I am.’ ’’

Parishioners responded with a standing ovation.

The reaction demonstrated how thoroughly Unni understands his congregation, said Rosaria Salerno, Boston’s city clerk, who has been a parishioner at St. Cecilia’s for some 30 years.

“I was on my feet, but too numb to be clapping,’’ said Salerno, a member of the parish’s advisory council. “I was just so numb that he had spoken with our voices, what each of us in those pews would have said.’’

Parishioners say Unni is a low-key, approachable guy who enjoys yanking weeds around the church property in Back Bay. Yet on Sunday, they say, he transforms into an electrifying speaker who paces the aisles during his homilies and who has a knack for making the teachings of the Bible relevant to modern life.

“He’s very good at explaining Catholic social justice teachings, which include inclusiveness,’’ said Mark Lippolt, a member of the parish council.

Unni’s father was a barber; his mother a hairdresser. He is a former English teacher at the old Christopher Columbus Catholic School in the North End, from 1983-85. He remembers making $150 a week as a teacher and being inspired to start his own landscaping business. But the priesthood kept gnawing at him.

The call to join the clergy “was not a thunderbolt, but a real presence inside me that grew as time went on,’’ Unni said. He entered the seminary in 1986 and later worked at parishes in Dorchester and Danvers before moving to St. Ann’s Church, near the campus of Northeastern University. He came to St. Cecilia about seven years ago, when St. Ann’s closed.

He recalls welcoming gay parishioners from the Jesuit Urban Center and says he never expected any problems when integrating a large group of gay and lesbian Catholics into his congregation.

“I think because sexuality is a part of this, it goes to the next level,’’ he said, reflecting on the current controversy. “I say: ‘Just come. I’m not going to stand in the way of your relationship with God.’ ’’

And Unni insists he’s not flouting church teachings.

“Jesus met people where they were at,’’ he said. “He went to them and reminded them who they were in God’s eyes.’’

Mark Arsenault can be reached at marsenault@globe.com.

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