A Roman Catholic bishop who resigned after claims of a love affair with a parishioner has admitted having had a sexual relationship but said he wanted to remain a priest.

Kieran Conry resigned as bishop of Arundel and Brighton last week after the estranged husband of one of the women with whom he was said to have had a relationship threatened to sue the church. The man had hired a private detective to follow his wife.

In an interview in the Sunday Times, Conry, 63, admitted to one previous sexual relationship. “I did wrong,” he said. “Celibacy may be a tradition rather than an article of faith but the vast majority of priests are faithful to their promise.”

Despite press reports of other affairs, Conry said he would do any job that came his way if he was allowed to remain in the church. “I’ve never regretted being a priest. I’ve never felt unhappy, I’ve enjoyed it and tried to do whatever was asked of me. I’ve always gone where I’ve been sent and I hope to do the same again,” he said.

Conry said his relationship with the woman whose husband threatened to sue was no more than a close friendship. The woman allegedly stayed at his house at least three times and they went shopping and visited the British Museum in London and a Henri Matisse exhibition together.

He admitted that a relationship six years ago had been sexual but would not say how long it had lasted. He said he decided to resign because “it was the easiest way to avoid further embarrassment, disappointment … and shame for the church”.

Conry said celibacy was not about sex but marriage. “When a priest makes a promise of celibacy, he promises to remain unmarried, that’s all. Then the ordinary rules of morality apply,” he said.

“But I’d like to make it clear I’m not calling for a change. I did wrong. Celibacy may be a tradition rather than an article of faith but the vast majority of priests are faithful to their promise, faithful to what the church expects of them. And I have great respect and admiration for that.”