At a council meeting last night, Bishop Tom Burns of the Diocese of Menevia told councillors about the Church's plans to demolish the chapel and use the land to build affordable housing.
The Church was closed in 2012, with parishioners instructed to worship at a newly refurbished church in Penparcau, approximately 20 minutes away.
This proposal caused backlash from a group known locally as Save Our St Winefride's.
The campaigners had appealed the decision three times, taking their complaint to the Vatican, each time the appeal was rejected.
Parishioners were enraged by the closure of the 1874 chapel, believing that the structure was not as unsafe as church officials had claimed.
There was also concerns raised about the new location of the alternate site, which is difficult for locals without a car to get to.
At last night's council meeting, Bishop Burns said: "I ask you to support an application for replacing St Winefride's. It means having to face demolishing it, and that is a huge, emotional and sensitive action to take, but I believe it is the only way ahead.
"Demolition of the church will release a valuable space in town, and a well-designed scheme will enhance the appearance of the conservation area."
Cllr Alun Williams responded: "You said that demolition of the church could actually enhance the conservation area. I would implore you not to use that argument again because it leads me to question everything you say."
One parishioner, Prof Frank Hogg, offered to pay for an independent structural survey to prove the building was safe.
"The costs of the survey would be paid by myself and a few well-wishers," Prof Hogg told the council.
"Such an independent structural survey offers a solution to the present disagreement."
The council passed Prof Hogg's proposal, further delaying plans to demolish the building.