In an open letter, the group said that celibacy causes 'fruitless loneliness' and 'social isolation' for many clergy members; particularly after retirement.
The group point to 1 Timothy 3:2 as a verse to "provide food for thought" which says "A church leader must be without fault; he must have only one wife."
The letter marks the 50th anniversary of the group's ordination and reviews the lessons they've learnt since entering the priesthood.
In the letter, the priests describe the isolation they feel because of their vow.
"What moves us is the experience of loneliness," the letter reads, "As elderly people who are unmarried because our office required this from us, we feel it vividly on some days after 50 years in the job. We agreed to this [form of] clerical life because of our job, we did not choose it."
The letter also suggests that the required vow prevents people from entering the priesthood. Priest numbers there have fallen from 29,000 in 1995 to about 15,000 today.
Retired priest Fr Franz Decker, who was one of the signatories, told local media: "We believe that requiring that every man who becomes a priest to remain celibate is not acceptable.
"We think, every Catholic should be allowed to choose if they would rather be celibate or not, regardless of whether they want to work as priests or not - just like in the Protestant Church or the Orthodox church, really, every church but the Catholic Church."
Clerical celibacy became a requirement in the Catholic Church in fourth century when the practice was introduce at The Council of Elvira.
Its canon 33 decreed: "Bishops, presbyters, deacons, and others with a position in the ministry are to abstain completely from sexual intercourse with their wives and from the procreation of children. If anyone disobeys, he shall be removed from the clerical office."