A petition has been circulated asking the Archbishop of Wales to set up a tribunal into the conduct of the Bishop of St David's, Carl Cooper.
The Bishop of St David's has not commented on the letter
A fortnight ago he announced that he and his wife were to separate after experiencing "difficulties" in their 25-year marriage.
He emphasised no one else was involved on either side and that they were committed to an amicable relationship.
The Bishop of St David's is not commenting on the letter.
Two priests have sent a letter to all the other priests in the St David's diocese asking them to support calls for a tribunal to be established which, according to the authors, would be an opportunity to probe a "perception of conduct giving just cause for scandal or offence".
The authors of the letter, the Reverend Will Strange and the Reverend Peter Jones, also made it clear they do not wish to prejudge the process and that they do not assume there is anything untoward to discover.
However, the petitioners stressed that failing to set up such a probe would be to accept a situation which, they claimed, "is causing distress among the diocese to many, both lay and ordained".
The two ministers behind the letter said that the procedures of the church should apply equally to all clergy of whatever rank.
Mr Strange and Mr Jones said that if they were in a comparable situation "we would be subject to the tribunal process at the Bishop's instigation".
They ended the letter by calling for an "united prayer for the Bishop and everyone personally involved in the situation."
A spokesperson for the Archbishop of Wales, Dr Barry Morgan, said that he had not received any letter signed by clerics calling for an investigation into the conduct of the Bishop of St David's.
However, the spokesperson added that: "the integrity of all clergy in the Church in Wales had to be above question and suspicion".
The spokesperson added that "any allegations of improper conduct...are investigated as a matter of course".
Under the constitution of the Church in Wales, the tribunal would ultimately have the power to remove Bishop Cooper from office.