Eleanor Cohen, the next Labour Mayor of Totnes, said she wouldn't go to remembrance services in church because she didn't "see that there's a need to go there".
She added it was unlikely she would attend any religious service. Pressed on the issue by local newspaper the Totnes Times, she said: "I don't know. It depends on the circumstances".
Ms Cohen had come under criticism for her decision during a council meeting.
Current Mayor Jacqi Hodgson asked her if she would take a lead role at events.
Ms Cohen said the question was outside the law because it implied the mayor had to conform to a particular religion.
Later she told the newspaper: "Simply to be there in your regalia just because people want you to be there and it means nothing to you would be hypocritical. People do this all the time and perhaps we should stop it.
"It's about people who died in war and gave their lives to protect others. That's what we should be thinking of and how to stop it happening again."
She accepted many mayors attend religious services despite their personal beliefs but said: "A lot of people do things without thinking all the time.
"We are a country where a very small percentage of people practise any religion, but we have an association between Church and State.
"Having looked at the Budget, there are very many other things to talk about like the dismantling of local government."
Nick Mckinnel, the Bishop of Plymouth, is quoted in the Plymouth Herald as saying: "I respect everybody's right to disagree over matters of faith and belief, but to hold public office means representing all members of the community, of all faiths, including Christian, and attending events which you might not always be in sympathy with or personally support."