City of Greater Bendigo councillor Elise Chapman says she does not have a problem with Muslims praying in Bendigo, but could not list a location she deems appropriate for a mosque.

Crs Chapman and Helen Leach objected to the Rowena Street proposal on Wednesday night amid claims from some residents the mosque would overthrow the Australian Constitution, increase violence in the region and see an influx of Islam believers "descend" on Bendigo.

Cr Chapman said she had based her opposition on planning matters, but "understood" concerns some women held about the safety of "our daughters and granddaughters", the Bendigo Advertiser reports.

She lives about 20 kilometres from the proposed site, "but if I lived next door, and given what you see in the media, maybe I would be [concerned about safety]," she said.

"People have a right to object."