Most also favour the ordination of women and more than three-quarters believe they should have the right to marry and have a family, a survey of more than 300 priests showed yesterday.
Many said they suffered profound loneliness and feel depressed because of their isolation.
More than half said they favoured the ordination of female clergy and said they would not object to the ordination of openly homosexual clergy.
Seven-hundred priests were approached as part of The Sunday Times survey, the results of which were published yesterday.
Of the 325 who responded, one of the largest snapshots of clerical attitudes for many years, 69% said they favoured the abolition of mandatory celibacy, 25% were against and the rest were undecided.
However, a spokesman for the Irish Bishops Conference last night rubbished the results, questioning the scientific validity of the survey.
“There are 6,500 diocesan and order priests and brothers in the country today. I don’t think this poll is representative,” spokesman Martin Long said.
“If the poll had been undertaken by a professional marketing company, and the proper sampling principles applied, then the samples would have been more reflective.
“I would question the professionalism of this poll and therefore, the results.”
The survey also showed that the majority, 58.1%, were in favour of women priests. A third of the priests surveyed were against any change. Respondents were split on the issue of homosexual clergy, with 44.9% in favour of the ordination of gay clergy, with 46.1% opposed.
Last week, outspoken Sligo priest Brendan Hoban said he was optimistic the Church could change and survive.
In his book, Change or Decay: Irish Catholicism in Crisis, published last week, 56-year-old Fr Hoban said implementing Vatican II, examining celibacy and the ordination of women priests and giving real power to lay people, were crucial for the Church to survive.
Vocations to the priesthood have been in decline over the last 10 years.
In 1996, 47 priests were ordained and 41 entered the seminary. Just one priest will be ordained in Dublin this year. No ordinations are expected next year.