The authority has been asked to scrap the prayers by a member of the public.
The complainant — who has not been identified by the council — says he or she finds prayers and religious ceremonies offensive.
In the letter the complainant says: "Where possible I avoid all religious ceremonies and it is intimidating to be forced to listen to prayers in order to exercise my right to attend meetings of the council."
Councillors meeting on Wednesday will consider whether prayers should continue to be said at meetings.
In the agenda for the meeting the council has published the views of several councillors consulted on the issue. None are identfied by name.
They show strong support for continuing with prayers.
One councillor said: "I feel very incensed regarding someone trying to stop me from focussing my thoughts so as to do the best in a Godly light for our own in north Devon."
Another responded: "As a Christian I feel threatened, intimidated and discriminated against by the views voiced in this letter. I would have no problem is prayers of other faiths were said alongside the Christian prayers."
Another councillor says the complainant sounds like "a career campaigner against all things religious" and suggests: "Have you Googled his/her name to see what show up?"
The council's assistant chief executive Don Pratt has suggested that the agendas for future council meetings should have the word Prayers before the word Agenda — to make clear that prayers precede the meeting and are not part of it.
● A complaint about prayers at Bideford Town Council meetings has been referred to the Standards Board for England.