The chaplain to the Bishop of St Davids says there is no truth in rumours about their relationship.
Bishop Carl Cooper and chaplain the Reverend Mandy Williams Potter (Library picture)
The Reverend Mandy Williams Potter is chaplain and communications officer to Bishop Carl Cooper.
It follows the bishop's announcement he was separating from his wife Joy after 25 years of marriage.
Mrs Williams Potter told BBC Wales that rumours in newspapers about her relationship with him were untrue and very distressing for both families.
Mrs Williams Potter is named in a number of UK newspapers, who refer to rumours surrounding her relationship with the bishop.
She said she was still living with her husband, though they were discussing a separation. No-one else was involved.
As the bishop's press officer, she said he had nothing to add to the letter to all diocesan clergy a fortnight ago, in which the bishop announced his separation.
He said in the letter that he and his wife had been experiencing "difficulties".
Earlier this week, two vicars in the diocese, the Reverend Will Strange and the Reverend Peter Jones, asked colleagues to petition the Archbishop of Wales for an investigation.
The Church in Wales has confirmed the archbishop has received a petition from clergy calling for an investigation into allegations about the conduct of Bishop Cooper.
A spokesman said it has been signed by a number of people and the Archbishop was now in discussion with those involved.
The letter said there was "great concern" at the speculation surrounding the bishop's marital breakdown.
It said it was a "painful subject" and they were "only too mindful" of the personal feelings, which the bishop had referred to in his letter to clergy.
"However leaving things to stand as they are, we believe, amounts to acquiescing in a cause of scandal and of offence to many in this diocese and beyond," says the letter.
"We urge you, therefore, for the sake of all concerned, including the welfare of this diocese, that these matters are investigated and dealt with according to the procedures set out in the constitution of the Church in Wales."
Bishop Cooper, who has three children aged 22, 20 and 17, has said he has no plans to resign from his post, following allegations about his private life.
He and his wife confirmed there was no one else involved on either side and they were committed to an amicable relationship.
"Regrettably, we write to inform you that we have experienced difficulties in our relationship with each other," the letter said.
"Sadly and tragically we have decided to separate. There is no-one else involved on either side.
At the time, the Archbishop of Wales, Dr Barry Morgan, said he was "enormously sad" to hear the news.
Bishop Cooper took up his post in St Davids in 2002.
As well as Pembrokeshire, the modern diocese also covers the counties of Ceredigion and Carmarthenshire and parts of Powys.